If you'd prefer a more interpersonal answer, take a moment to remember why these words exist...
While I'm sure it's unpleasant to be accused of homophobic or transphobic ideas or behavior, it's arguably much more unpleasant to be on the receiving end of those ideas and those behaviors. Most LGBT+ folks can relate some pretty horrifying stories about how it has touched their lives.
My best friend's partner lost his little sister in The Pulse nightclub shooting in Orlando, FL. When I think about homophobia, I remember that day. I remember my community collectively weeping.
I also remember going to a candlelight vigil a few days later, in a smaller central Florida city. LGBT+ folks, allies, friends, and family from all over the state had gathered to mourn in a local park. On the way into the park and on the way out of the park we had to walk past a line of Sheriff's deputies who were supposed to be there to "protect" the gathering, but could be heard cracking jokes and sneering at us.
I remember going on my first date with a non-cis person and seeing the other bar patrons recoil at the sight of us. I remember the bartender pointing me out and calling me a "faggot" the next time I went to play darts there on my own.
I remember my partner sobbing when their mother didn't want them to attend the family Christmas party.
I remember walking down the sidewalk holding hands with my partner and having someone throw a glass bottle at us from a speeding car.
I remember all the fights and taunting in parking lots after school.
I remember my good friend, that had the courage to come out back then, having the word "fag" painted on his car, by a co-worker, and him being told to "keep quiet, or look for a new job"
You probably don't want to be associated with something that causes so much pain in the world. But neither do I. Neither do we. It isn't just a difference of opinion, this really affects our lives. So, admittedly it's hard not to take offence when someone wants to make a semantic argument and, more or less, compare being called homophobic or transphobic to the experience of having to live under the weight of those things.
If you don't like the implications of being -phobic, try to understand. Try to empathize. Try not to make people feel awful for simply being who they are and loving who they love... Or, failing that, just try to coexist and leave us in peace.