More like a built-up response for years of attempting to erase all the religious significance of the holiday and replace it with generic consumerism.

That's exactly the point. The holiday didn't lose any of its religious significance in private worship, or within Christian churches. What happened is that in secular spaces - workplaces and retail stores and other institutions - the people who operated those secular spaces moved away from presenting it as a religious matter and instead a more "generic" celebration. Again, because not everyone in those secular spaces was Christian or observed Christmas.

So Christians aren't allowed to loudly proclaim their faith on one of their most holy days?

They are absolutely allowed to. No one thinks its wrong for a Christian to proclaim how excited or devoted they are to the celebration of the birth of their deity.

But that's different than debates over whether the big department store in town should greet their customers with "Merry Christmas" versus "Happy Holidays." It's one thing to proclaim your own faith; it's another matter to interact with people in a way that assumes/presumes that they share your faith, or want to participate in a religious (as opposed to "generic consumerist") observation.