I don't see how we even have a "problem" at all.
I think that is the fundamental divide that SE does not seem to understand and why their whole "welcoming" move is met by so much resistance and frustration.
On one hand, we have the technical sites. Those are there to answer User1248346's programming problem. Background is not required nor requested. Whether that user is a man or woman, in the Swiss alps or at an Indonesian beach, married or single, we will never know. Because it does not matter. In fact, sharing that information would be weird. Their compiler will always work the same. Put in the correct code, you get the correct result.
People on those sites don't really see the problem (literally, they don't see it because there is nothing to see, not because they turn a blind eye) and feel very insulted when told they are not welcoming. They are providing free services to random strangers and they are told that their biggest flaw is that they treat every one of those strangers like they would treat a white, straight male, the most privileged class on the planet. So they wonder what the hell this is all about, being told that they are bad people and need to be more welcoming than "just" treating random strangers like their equals and providing free work and education. How much more welcoming would you like your volunteers?
And then... there are the other sites on the network. Where people need to identify in turn to solve their problem. Because their problem is very dependent on all those factors. Background. Gender. Religion. Culture. And I will believe everyone that says they do not feel welcomed there. On technical sites you get an answer that is verifiably true (you compile it and it works... or not) whether you like it or not, it's helpful. On those other sites you get opinions or in the best case experiences. While my compiler and your compiler are guaranteed to do the same thing (given same versions and settings), whether my parents react the same as your parents when my long lost aunt tells them their nephew is gay... is really not an exact science and bound to be a big ball of communication problems, cultural misunderstandings and all round opportunities to get bad vibes. If someone explains how to fix my program in broken English, there are only a very few options to get that so wrong to be insulted. To explain your views on LGBT people without insulting any of the multiple sides to this is hard even in your native language. So yes, if someone says they do not feel good about how this is handled, I'd give them the benefit of the doubt and say: on those sites? Absolutely. I have not witnessed anything specific, but I will believe you that this can happen easily, frequently and in ways I probably would not even notice.
The fundamental problem is that SE mixes all of this into one big bowl of telling their users they are all bigots and they need to improve if they don't want to be banned.
I will support the improve part, but I will not silently agree to the bigot part. It's a little like asking "Will you stop beating your wife?". I certainly support not beating anybody, but I will not agree to "stop beating my wife" because that never happened in the first place and mixing me in with the criminal **** who do that is not going to get any support from me and seeing the reactions, a lot of people like me.
So yes, from my perspective, not seeing the problem at some places, does not mean they don't fester in others. But SE does a terrible job at telling them apart, losing some very valuable support they could have gathered. I don't think any of the opposed users would oppose a "stop bigots from abusing people" campaign. Almost all oppose a "Chances are you are a bigot, stop that behavior" campaign, because that is not the truth and I personally feel very offended by it.
A practical example: as a technical user, I have spent years discussing problems with users like BlackUnicorn73 or HazMatX or User1234567. Telling me I have to respect their correct gender pronouns sounds ridiculous. I don't even know those. I don't know if they know them. Or care. If any of them had corrected me in the use of the one's I estimated, I would have complied. I don't care how exactly I address any of them. But making a rule about that, a code of conduct with consequences to follow? Seems very far fetched from that perspective.
On the other hand side, if you are on a site that is non-scientific and someone intentionally uses the wrong pronoun to constantly harass you against your expressed wish? Sure. Ban their sorry behind. I don't care and I certainly won't oppose that or support harassment.
But the difference here is the intention behind it. The vast majority does not belong to the later group and SE completely fails to recognize that.
So to summarize: Yes, it perfectly possible that for a large amount of users, this problem is not visible, because it does not exist as a global constant. And there is nothing wrong with that. It is also correct to say that for some user's, this is a problem.
And we could all be happily working on a solution for a better site, if this divide would be recognized.