I was tempted to write an article reply, but I want to stick to stories, so I just wrote you a HUGE comment instead. 😝
I'm more troubled by a kind of Orwellian horror at the thought of the government banning a peaceful religious holiday than thinking about how I'll manage to enjoy twinkly lights and presents under another name.
I read the "Should We Get Rid of Christmas?" article, and I think it's mostly a criticism of shared holidays. Thanksgiving is infamous for causing family tensions and is the definition of a turkey dinner. Valentine's Day comes with unwanted gifts. St. Patrick's Day results in a lot of car crashes. Debt is kind of a good argument, but is more of an argument for better wages and financial education.
Christmas sure does disrupt ordinary life in December--that's the point. Winter is dark and cold, which is why the Germans (Yule) and Romans (Saturnalia) had big, bright celebrations in the middle of it. A lot of people get seasonal affective disorder. I've heard arguments that January needs a holiday in the middle to make it less gloomy.
But what I think is at the heart of antagonism concerning Christmas is the dual sentiment that we are tired of serious Christians, and that the time of the white middle-class Westerner is up. Case in point, the solstice celebration you described sounded very similar to Christmas. And since the involved groups are minorities, there is no such attack on Hanukkah or Kwanzaa.
I am sympathetic to people who are tired of the white majority running the show, especially when they feel left out or guilty, but I don't think calling for the cancellation of the majority's celebrations is a great solution--or even a solution. Majorities are still human beings; in fact, they're most human beings. If we want to take away their religious celebrations, I have to ask what is so inhuman about them that that's a just move compared to culturally canceling a minority's religious holiday.
On another note, for many people, Christmas has nothing to do with Christ. It's a big holiday in Japan, whose population is roughly 1% Christian. I mean, it's a pretty good holiday; lots of non-Christian people have taken it on. Día de los Muertos is gaining popularity in the US; that's culture-blending at work. Lovely!
So if people are annoyed at this big Christian celebration, it's worth considering that just because it comes from religious roots doesn't mean that it can't shift meaning under the same name as the world evolves. Non-Christians who voluntarily celebrate Christmas are proof of that. To me, "BC/AD" or "Christmas" have strong historical roots that in themselves justify existence as-is, the same way that the Bible is a remarkable blend of myth and history. Changing names is just playing semantic games. Regardless of its flavor, history shouldn't be buried.
To back up and close, it remains a religious holiday to many people. That has to be in discussions of keeping or doing away with Christmas. (If one thinks it should be canceled regardless of those people's feelings, I can dig it, but that requires some major backup arguments that would necessitate a full-scale cultural attack on all religion. Not so neat and easy as "let's cancel Christmas.") As an atheist, I think religious people are living in a little bit of a dream world, but freedom of peaceful expression is far more important to me.