Agree on your first paragraph.
But your statements about DOMA and DADT fundamentally misrepresent the events of that time. Bill Clinton signed DOMA because the Republican Congress had passed it with veto-proof majorities. To that statement you might reply, "Well, didn't they need Democratic votes for a veto-proof majority?" and "Couldn't he have vetoed it symbolically? Solidarity!" At this point, however, you have to consider the context. 1996 looked very different from 2018, or even 2004, when gay marriage became the hot-button issue again.
Only 27% of people favored same-sex marriage at the time. It would've been a hill upon which to die for many Democrats, especially since they couldn't have prevented its passage, and Clinton would've faced tremendous blowback for vetoing it. You really think President Dole would've been nicer? (Fun fact: Nancy Pelosi, favorite target of the ~~~true progressives~~~, voted against it.)
The entire episode actually offers an argument for supporting Democrats even if you disagree with them. Did all Democrats support gay marriage at the time? No. But the bill
never would've been brought to a vote in a Democratic House or Senate. Enough of the party supported LGBT rights at the time; they just couldn't say so openly or always vote that way. DOMA, as well as a bunch of other nasty bills, can be linked directly to the 1994 midterms, when Republicans took control. I can say with certainty that LGBT people's situation wouldn't have gotten
worse under a Democratic Congress.