It's easy to find Democrats talking about the importance of fatherhood, and that's backed up by public policy: for instance, a goal of Paid Family Leave is ensuring that fathers have time with new children, not just mothers.
It's harder to find Democrats extolling the virtues of two-parent families. But that's no surprise: "two-parent family" is coded right-wing, and politically involves not just the importance of kids having two parents, but also of pushing back on equity in the workplace for women, or benefits for single parents (and, if you go far enough back, say to the 1970s and 1980s, towards liberalized divorce laws).
So I think the claim that liberals avoid talking about family values fails. They use different language than conservatives, but that's just how politics works. You can exploit the semiotics of political messaging to paint either side any way you want, but the idea that liberals are opposed to two-parent households is inconsistent with what liberals advocate for.
An appeal to what gets shouted down on Facebook groups† also isn't persuasive. First, note that you didn't get shouted down for saying that fathers are important (which is how you'd code an appeal to two-parent child-rearing --- single-parent households in the US are overwhelmingly, like >85%, led by mothers). But also: Facebook groups are cliques. There are popular Facebook groups in Oak Park that would ban you for arguing against abolishing the police. But defunding the police failed on our last ballot by something like 70-30. Biden carried our precincts overwhelmingly; by a far higher margin than Cook County as a whole.
Finally, for all you're saying about the downwind effects of elite liberal take-havers saying it's OK to pursue single parenthood, in context what you're trying to say is "violent crime statistics that prominently feature Black people is a natural consequence of liberals de-emphasizing two-parent households". I'm sorry, that's plainly false. None of the circumstances this thread talks about have anything to do with BLM talking about people being raised in part by aunties and grandmas, or anything said on Twitter.
I said upthread and I'll say it again: it wouldn't be fair for me to try to paint conservative thought by what Sohrab Ahmari believes, let alone Marjorie Taylor Greene. But that's effectively what you're doing when you suggest that BLM-Facebook-thought defines liberalism. Liberals overwhelmingly believe in the importance of two-parent child-rearing.
† (As someone somewhat active in local politics, I'll add that Facebook is deeply problematic --- it stands in for public comment and discussion, but provides none of the safeguards of open meetings laws. There's also a trend towards municipalities outsourcing this kind of discussion to platforms like Granicus, with the same problems: private entities can control public speech, which is fine until they become the government's own formal mechanism for collecting feedback. It's a whole can of worms.)