As far as cultural/social issues, yeah I don't think Trump cares either way about a lot of them. It's more an issue of the people he surrounds himself with and that he's easily-influenced. I definitely wouldn't call him a "progressive" on them just because he hasn't personally worked to ban same-sex marriage though. And yeah, Obama/Hillary were not for issues like that for a while, but it always seemed like a factor of them waiting for it to become popular enough that it wouldn't hurt them politically. I mean, I'm pretty sure Obama's not even religious lol. But going outside the norm on that wouldn't help him, at least at the time.
To be clear though, I'm not just talking about progressive policies within social issues. Tax cuts for the rich are deeply unpopular, for example, while a number of other proposals on public services have very strong support. MFA is already over 50% depending on polling, and MFA (or universal healthcare in general) support will likely keep trending upward.
With identity politics, I actually agree that it's not as favorable as the narrative we're fed. But I'd argue it's actually more of a moderate-left thing than a far-left thing. There's an extent to which representation matters and no politician should be held back by their race/gender/religion/etc. But the progressive wing is espousing policy first and foremost. Their main candidate is an old straight white male. Meanwhile, we've seen tons of establishment pushes for POC or female candidates with their identity as a main factor over any talk about their policies.
And yeah I get those policy platforms for Trump, and it's a good strategy to run a populist campaign on issues like that, that can cross party lines in a myriad of ways. But both his rhetoric and tactics in those issues are very much open to criticism, regardless of what you personally believe. So against a candidate who can at least somewhat match his populism and promise more than status quo policy, he would be very vulnerable before we even get to Trump's personal drawbacks.