I think what bothers them is the implied assumption of cultural/religious uniformity. For at least six weeks of the year the common American culture is largely taken over by a Christian holiday, and non-Christians who don’t celebrate Christmas (and, for that matter, Christians who don’t want Christmas treated as a generic/secular holiday) are expected just to put up with the constant barrage of Christmas themes in public and commercial spaces of all kinds.
It’s not that “said religion is in plain view of others”; I don’t know of any non-Christian who objects to, say, the distinctive architecture of churches or the fact that churches are all over American neighborhoods, or the fact that nuns and priests walk around in distinctive clothing, or the fact that lots of Christians openly assemble at church on Sunday mornings. It’s the fact that the Christian holiday of Christmas just takes over so many aspects of American life for so long a time; “having that stuff rammed down our throats for months”, as Clothahump put it.
Of course, the real problem is not with Christianity or Christians but with the bastardization of the Christmas holiday that’s taken place over the past century or so. Christmas remains an important Christian sacred holiday, but it’s also been exploited to the point of ass-raping by commercial interests who make loads of money off it because it’s traditionally associated with feasting and present-giving.
Christmas the festival of Christ’s birth and Christmas the commercial cash cow are inextricably entangled in a sort of monstrous hybrid. Many of its themes and symbols are still Christian enough that non-Christians often feel excluded by them, and they’re so ubiquitous even in commercial/secular contexts that it’s often difficult for non-Christians just to ignore them.
Hence the feeling of resentment and pissed-off-ness that is ignited in many otherwise very tolerant and friendly people during the “season of peace and goodwill”.
