I agree OP that being proud of an accident of history over which you have no control is odd. Proud of an achievement - yes. So proud of overcoming prejudice, yes. Connected to, open about, interested in your roots, yes.
I do understand though, how 'pride' has come about as the opposite of others' attempts to enforce shame. 'Open and proud', with an obvious parallel to being 'out and proud' - embracing another accident of birth over which no-one has any control but about which we widely accept people expessing 'pride'. It's an expression of identity - or solidarity with others', in this case ancestors', identity.
On the face of it though, I find it odd when some people I know bang on about being 'proud' that their parents were working class. I would understand pride in achievement e.g. overcoming adversity and bringing up a lovely family, giving their children good opportunities, despite hardship. That isn't how it's expressed though. It's about 'being' not doing.
What's really odd is that the people who say this have become blatantly, self-acknowledgedly middle class themselves, so are rightly proud of their own achievements in escaping the economic constraints of a WC life. They weren't 'proud' enough about their parents' WC identity to choose to embrace and perpetuate it for themselves (and why should they). They found being comfortably off professionals, better. Which makes their pride in their parents' class per se, rather than their achievements, sound very patronising, or just absurd.
Personally I'm not going to claim pride in anything I haven't achieved. Nor am I going to feel shame, on a personal level, over anything others' did, in the past, over which I had no control. As a member of a society that continues to benefit from past degradations of others and plundering of their resources though, there is a responsibility at a societal, political level to acknowledge how past actions have influenced where we are today and particularly, how and where the attitudes that enabled that to happen, continue to play out. So, I think our responsibility is for the present and future but we should learn from the past.
Pride and responsibility for the past actions of others inhabiting the same land can cause all sorts of trouble and confusion. But, pride and responsibility for political structures and ideas that have a long history but which exist now, does make sense and is important. Part of that is discarding the ideas and practices we cannot take pride in now.