Apologizing can, in fact, win people over _if_ authentic and followed up by appropriate action.
One recent incident I've been tracking jumps immediately to mind.
Recently, a D&D streamcast, Critical Role, decided to participate in a Wendy's promotion, to the horror of their fanbase which largely eschews big corporations and their _marginal_ (in all senses of the word ;-) ) food products. A vocal contingent of the community felt this promotion was not at all aligned with the progressive values of the streamcast and community, and they let the org have it!
Within 24 hours, the Chief Creative Officer (and general face of the stream) apologized, and the org announced it was donating all its profits to a charity supporting farm workers.
Sure, there were a couple of angry people who were still not satisfied, and there are probably unpleasant longer-term consequences with potential future advertisers that they will have to deal with. But, in large part because they pay careful and compassionate attention to their community, you could see that the bulk of the community immediately jumped back on board.
Do not let Trump erode your sense of what is right for your product, company, and community. The dark side, after all, is not more powerful – only easier and more seductive.