Is redistribution of wealth, aided by social institutions, from the top down wrong, but from up from the lower strata to the top OK?
Wealth is not "distributed". Wealth is created and destroyed. But it is not "distributed".
When you forcibly "redistribute" wealth, that involves stealing the wealth that someone has rightfully earned, and giving it to someone who has not earned it. Yes, that is wrong. If I come to your home and steal your stuff, you would call the police, arguably because you think your wealth being redistributed to me, is wrong.
Bottom up wealth redistribution, doesn't exist. Poor people learning a skill, and working a higher paying job, is not 'redistribution'. It is simply people creating more wealth, and thus earning more, thus having more.
Yes, that's ok. In fact, I encourage it.