In regards to a and b, wouldn't someone who thinks the former likely be someone who also thinks the latter? Those don't seem contradictory and, indeed, one is a possible explanation of the other.
People who lean right, tend to think movement from lower classes to higher classes is possible with hard work and that a person’s starting point doesn’t matter as much.
People who lean left tend to think where you start is the biggest predictor of where you will end up regardless of how hard you work. Hence the reasons one side favors the social safety net more than the other side does.
That has been my observation at least.
So they don't exactly disagree on what the circumstances for success looks like as much as they disagree on the degree to which those circumstances are under an individual's control.