I've more or less been here too. The thing that helped the most was to try learning more. Why do people think xyz? Let me research the socioeconomic factors of this area & learn about the tenets of that belief. Or just talk to them, you know. At least ~75% of the time, if someone says something out of pocket & I ask them why they said that, it immediately becomes clear that they haven't thought about it deeply at all. A disturbingly large amount of people believe something because they heard some guy say it once. It's frustrating, but mostly just sad that people are not as educated as I had the opportunity to be, and don't seek it out. There's not always much you can do about it besides making them feel heard and encouraging doing their own research (ACTUAL research though, not confirmation bias).
No offense to you, much credit to you in fact for realizing this is an issue, but it seems like your change in mindset came from being personally affected by it. As in "if I'm gay, it must be OK I guess". To continue down your path of enlightenment, it helps to try to gain understanding of their situation & position regardless of your position. This can be particularly difficult if you ARE personally affected by it, such as people being demeaning to gay people, but it gets easier if you practice.
The thing that gets to me the most these days is people who are closed minded. Trying to be objective can help determine if the issue even matters at all, but going too far down the oath of objectivity betrays your desire for everything to be explainable and have a yes or no answer. Life, unfortunately, is not often like that. Sometimes it is, or gets close. Murder is bad. But even then, what if the guy you murdered was planning on doing something worse than killing one specific person? What if he already had? I can say "we as a society cannot accept vigilantism" while simultaneously not saying anything if I witness a known child rapist getting shot. Both diametrically opposed actions can be morally correct.
Humans love labels. They love assigning it to themselves even. The way I started to be able to grt around this is to learn more about the person to discover what kind of person they ACTUALLY are. Think of it as a fun project. Some conservatives, for example, will be the first to help you if you need a truck to move or need food. Some are part of strong unions. They are still culpable for how they vote, but boot licking corporations & victim blaming the poor is not necessarily who they ARE.
How do I avoid labels for myself? I don't worry about it so much. I can be labeled if it helps someone, or I can not be. The important thing to remember is that the actions of people who exist under the label define the label. The label doesn't define you.
Even the same label can have opposite effects or meanings in some situations. To some, being a feminist is simply treating women as fellow human beings, and a prerequisite to being a decent person. To others, it is a mask for misandry. So sure, I can be a feminist. But I will probably not advertise that label to a man whose mother abused him as a child and favored his sister under the guise of feminism. What matters is what you actually DO. Are you there for your friend who was abused? Do you respect women? Yes? Then that's what matters, not if I call myself a feminist or avoid it.