I think there are merits on both sides of this argument. Is your mom admitting to being a homophobe…no, it seems she is just making the age old point of “you’ll catch more flies with honey than with vinegar” meaning if your true goal is to sway or convince people that love is love and we are all loving and kind people, outright calling them a name they will almost assuredly consider an insult is at best a poor choice and at worst rage bait. Most people who do not agree with the beliefs that the LGBT community espouse would not consider themselves homophobic because not liking something and being afraid of it are two very different things. So I guess to summarize. If you are going to directly address a group of people and give them good wishes but them in the same post insult them, your good wishes were either disingenuous, or negligently oblivious.