How to engage the reconstructionist / historical-based pagan and not get your feelings hurt:

Lesson 1: Learn to discern the differences between fact and opinion, history and UPG/experience.

You may not have realised that you were presenting a subjective statement as an objective one.  Especially in the United States, the stress on this aspect of language arts in schools is often failing, but so if pop culture, to be frank.

Facts, are ostensibly objective statements subject to verification by external sources.  Sometimes the factuality of a statement is presumed (due to either lacking or misunderstand the data), but is later proved false by external data --the statement, due to being presented that way, is still considered a statement of fact.

Opinions are ostensibly subjective statements that cannot justifiably be proved true or false with external data.  Some articles may present very clear opinions "factually" for humorous effect, like "It's a proven fact that Breyer's Ice Cream is better than Ben & Jerry's", but if the context is understood, then it's clear that this does not need to be, nor can it reasonably be verified by external data.  Now, a lot of people like to justify their opinions with facts, like "Breyer's ice cream is better because they sell their ice cream in larger quantities and don't use carageenan, so it's a better value for the price and doesn't adversely affect insulin levels", this would be an informed opinion, and still exists separately from the facts --the facts, given the ice cream brand example, are simply that you can buy Breyer's ice cream in larger quantities than Ben & Jerry's and that Breyer's typically doesn't use carageenan, but the statement that this makes it "better" as an ice cream is still subjective --maybe you don't like to have huge quantities of ice cream sitting around, or maybe carageenan doesn't affect your insulin, or maybe you have other reasons to prefer Ben & Jerry's.

Informed opinions are also a staple of many professional fields.  A doctor's diagnosis is an informed opinion based on the facts of your symptoms, both verified either visually or with testing, and symptoms reported by yourself (like localised pain, which is harder to verify).  Another doctor may have a different opinion, but it would be no less informed than that of the first doctor.  Archaeology and anthropology, both fields very important to religious reconstruction, are also filled with informed, professional opinions.  These opinions are often presumed factual, not only by laity from outside the fields, but by others within the fields who accept them as factual.  People who are professionals in one field, like Carl Jung held in psychology, cannot justifiably hold an informed opinion outside that field, like ancient religions; that background will necessarily inform one's opinions in outside fields, which simply isn't the same as a psychologist's informed opinion of psychological topics.

Lesson 2:  There are subtle differences between appropriation and acculturation.

If you've been on Tumblr any time since about 2009, you're probably familiar with the "zero tolerance" policy that many teen Tumblring pagans have adopted toward "cultural appropriation" while hardly able to articulate an adequate definition of what that even means.  This is in large part due to students of humanities going on the Internet, blogging about things, and then younger people read those blogs, but lack the background to really grasp what these things are about.  Sometimes said students barely understand, either, but cos they read Foucault and masturbate furiously, they don't care, "cos grades were just created by society to try and make you feel bad" about what you think you understand, or something like that.  (As an aside:  If a self-proclaimed "Classicist" ever favourably cites Foucault, run.) 

Basically, the definition of "cultural appropriation" that most people use in a negative light is the uninformed, superficial, wanton used of cultural trappings of a minority culture one does not belong to.  "Appropriation" often includes the practise of some white people claiming to be "Native American spiritualists" or similar, while spouting "facts" that people actually from those cultures dispute.  Basically, it's reworking a minority culture to fit one's own purposes and ideas, which may not have anything to do with what that culture's language, tools, or garments may signify in their proper cultural context.

On the other hand, acculturation is when people from one culture become one with another culture, to varying degrees; to absorb oneself completely into the other culture is assimilation.  Acculturation is necessarily informed.  As an example:  Lord Byron was so in love with Hellenic culture that some argue he was fully assimilated Greek when he joined in the Greek War of Independence, others argue that he was simply highly acculturated into Greekness.  Acculturation is also arguably syncretic, especially when practising ancient religions and reconstructing that continuum between ancient and modern practise, because it is necessary to blend one's native culture into a religion when that religion comes from an ancient culture where it was clearly interwoven into one's way of life.  "Recons", traditionalists, or historic-based pagans (or whatever other terms one may use), tend to aim for some degree of acculturation, even if they still largely keep to their native culture, being clearly informed of the acclimated culture should be apparent, especially to those of that culture or similarly acculturated.

That said, there's also a difference between informed eclecticism and acculturation.

Lesson 3: Eclecticism is NOT a dirty word.

While certainly come historic-based pagans need to remember this, as well, it'd be really nice if everybody could remember it.  Eclecticism is simply what happens when one places less importance on history and acculturation than on "what works for [oneself]".  Eclectism is necessarily a very personal take on religious paganism that pulls from all sorts of sources, ancient, modern, Medaeival, folkloric, philosophical, and so on.  Carl Jung, or at least quasi-Jungian interpretations of religious concepts tend to be popular with eclectics, but not with traditionalists.  Joseph Campbell's ideas also tend to be incredibly popular with eclectics but again, traditionalists give him less credit.  Jung and Campbell's ideas are based largely on their own, wholly modern notions and are clearly held as outsiders to the religions that they've analysed to fit these hypotheses, and tend to be at clear odds with a logical continuum from the traditions as maintained by practitioners of said religions.  On the other hand, if you believe that Jung and Campbell were on to something, and that their ideas are more relevant to the religion you want to practise, that's totally fine.  Most traditionalists won't even be bothered by spirited debate, but my still take pause if you claim to be of the same religion --it'd be like saying Mormons (a very new Christian movement) are Gnostics (which is, for all intents and purposes, a collective of reconstructed Ante-Nicean Christianity), just because some of their ideas overlap on a Venn diagram.

It's perfectly OK to be Eclectic.  Any presumed derision of Eclectism from historic-based pagans is largely blown out of proportion, and has only been seriously applied by a relative handful.  While some may justify derisive statements made toward eclectics, like citing that the average non-pagan can't tell the difference and this "makes us all look bad", I have no personal quarrel with stating that those people need to take their head out of their bums.

Lesson 4:  Don't take it personally.

This is easier said than done, I know.  I'm not innocent of taking things more personally than necessary, and my advice may not work for you, but some of it may, or may at least work for others.

There are differences between personal insults and asking questions when perceptions clash.  Suggesting your practises might be eclectic may be more likely a recommendation to reflect on the words you may be using, and how that differs with the historically established practises of that tradition, regardless of whether or not you consider yourself "recon".

When I find myself about the have a completely emotional response to what I just read, I step away from it.  I find a distraction for a few minutes to an hour or two, then consider what I just read, does it need an emotional response, or is it best approached with reason, logic, facts, and maybe a bit of humour?  It's usually the latter.  Emotions can be a powerful thing, they're a gift from the gods, in my opinion, but like all gifts, they're best used wisely --your mother may have given you a lovely dress and gorgeous double cuffed shirt with cufflinks, but you wouldn't wear either to run track, would you?  I certainly wouldn't.  If the Internet has taught us nothing else, it's that emotional responses to blog posts seldom go over very well.  Even the pseudo-sociology crowd has rarely made good from being as emotional as they can get on Tumblr.

If I approach what I read more rationally, it's usually a lot easier to tell if the statements made were clearly made to insult me or my tribe.  It's not always an exact science, and it takes some trial and error.

Part three is going to address some of the more common accusations I see lobbbed at recons.