There's always nuance, irrespective of whether some position is right.
Gay rights, for instance: what are you talking about, exactly?
I don't know what happened in your conversation to make your interlocutors doubt your sincerity, but perhaps it had something to do with being unable to inhabit the point of view of someone with whom you disagree? Did you listen to them, or sputter and get angry?
For me, it's hard to overstate how much I support the right of people to be gay and have homosexual relationships (which are not the same thing, but I support them both). My perspective is that full social acceptance about homosexuality is a no-brainer. An ideal world would place no special emphasis on it, any more than a straight relationship. To my mind, having any negative opinion about it at all is reactionary and ignorant. And yet, there's nuance.
The State should have no opinion on nor legal category of marriage at all, either, IMO. "Gay marriage" should not be something that's legal or illegal, because neither should "straight marriage" be. Strictly, I don't support "gay marriage", not because of the "gay" but because of the "marriage". Imagine someone who agrees with my stance on "gay rights" but without nuance screaming at me because I don't support "gay marriage".
My support of homosexuality is part of a broader support for consent in general: just as no one ideally should have a say about whether 2 men have a homosexual relationship, no one ideally should have a say on whether sexual or romantic consent involves exchange of money. Every argument for homosexuality (or marriage) can also apply to prostitution, and it's unprincipled not to recognize that. Imagine someone without nuance screaming at me because I'm comparing homosexuality to prostitution.
Let's see how far down the rabbit hole goes.
The Westboro Baptist Church (WBC) is a small sect that gets a lot of publicity in the United States for holding protests against homosexuality, involving holding up signs that say "God hates ". It's hard to overstate how much I disagree with them about homosexuality, or anything, really, as an atheist. But what is the deal, there? Are they just homophobes? Is there rampant, latent desires amongst the congregation? There are lots and lots of articles talking about what they believe, and their Wikipedia page labels them as a hate group. But what do they say themselves about what they believe? Let us use them as an object lesson, to see how one might come, not to agreement, but at least to understanding, one's political opposition.
They are a modern church, living in the 21st century, and they have a website. I won't link to it, because the URL has a slur, but I spent quite a lot of time on their website, inhabiting their beliefs, laying aside judgment, just to really understand what's going on. It's hard to summarize it all, but a single quote from their FAQ is instructive:
Q: I was taught that the Bible says that God loves everyone. Why do you say that God hates people?
A: The Bible teaches that God hates people. The notion that "God hates the sin but loves the sinner" is unbiblical. For example: “Thou hatest all workers of iniquity.” (Psalm 5:5). Here is a list of additional Bible examples of the hatred of God towards people....
To understand - and remember, this is not about understanding WBC
per se, but about exploring this concept of nuance even about something we both agree fervently - to understand what the WBC is saying, here, it's necessary to really
inhabit this idea that: a) The Bible is a guidebook on how to get into Heaven. b) God, not humanity, defines what is good and wholesome c) The consequences for misinterpreting this guidebook are literally catastrophic.
That you and I do not share these beliefs is not the point. That we might find them abhorrent misses the point. This is the world that these people inhabit: God is a real and terrifying force that will torment you for all eternity for even slight transgressions of a cryptic, contradictory set of rules. To their mind, these protests are a kindly, generous act, to literally save people from eternal torment.
These congregants live their lives under the thumb of a cruel, capricious, supernatural tyrant. I, personally, cannot bring myself to feel anger towards them. Only genuine horror and pity, that they inhabit such a world view.
Now, circling back to the beginning, a rhetorical question: Can you, yourself, describe why you support "gay rights"? If you cannot get beyond "there is no nuance, it's just right", it could be that you come off as insincere because you accept no challenges to your perspective. Are you afraid that you might hear something that would change your mind? If not, be generous to your opposition, hear them out. Inhabit their perspective. Mull it over. There's really nothing to be afraid of.