Thanks for reading. Funnily enough, I have written a "War on Christmas" article too, some years ago, also on Medium :)
I'm Jewish — both parents, so I was raised Jewish, without celebrating Christmas, and the same was true for a number of kids I grew up with. My identity affects my perception of the faux outrage over the (nonexistent) War on Christmas.
If a stranger wishes me a Merry Christmas, I'm not mad at them; I recognize it's most likely a casual friendly gesture based on an incorrect assumption about me and not primarily an attempt to impose Christianity on a Jew. I might nod, smile, wish them a "merry Christmas too," and/or "happy holidays," and be on my way. I probably won't inform them I'm Jewish and/or atheist unless I decide they're entitled to that personal information about me or I decide it's otherwise appropriate to the moment to give them an opportunity to reflect.
Anyway — yes, a person does avoid conflict when reassuring someone else that whatever they said was excellent as long as they meant well. People like to be reassured that others perceive them as essentially good and well-meaning. People also like to be agreed with. If someone says something, and I say "Great, I agree," I have prevented us from being in conflict.
However, if someone wishes me "Merry Christmas" and also — knowing that I'm a Jew, a secular liberal, etc. — understands themselves to be thereby deliberately initiating conflict with me (in other words, they're playing the War on Christmas game and pretending to be the victim), I don't feel it's my responsibility to reassure them that they mean well, because in that case, they don't. They're being aggressive. I might just say: I don't celebrate Christmas, but I'm not fighting a war on Christmas. Because both of those statements are true. When I deny that secular Jewish liberals are waging war on Christmas, the other person might interpret me as causing or prolonging conflict simply because I disagree with a statement they've made about the Jews. At that point, pragmatically, yes, it may be best for me to soothe their feelings and walk away — but morally, the responsibility should fall on them to stop acting this way. I would be doing extra work to make them stop feeling upset (or make them stop pretending to feel upset). I might have a reason to do that, if only so I can get on with my day, but then the burden of the interaction has fallen on me to manage a stranger's feelings/behavior, and ultimately that does not translate to a gesture of goodwill that helps me relax and enjoy a holiday. That's just a stranger reminding me that Christianity is the dominant religion in our culture (as if I might have otherwise forgotten).