A regressive system takes away from those that don't have much to give to people that already have a lot.
In this way - a blanket statement of guaranteeing the top x% of students admission into state schools is - I would argue fair and reasonable - but I would also argue is regressive.
This is assuming the top x% of students come from wealthier & more educated families. It's possible this assumption isn't true.
I think progressive policies would be like those that make it easier for certain groups to get admitted (i.e. harder for other groups). This seems unfair, but if you want change, I don't see how you do it fairly.
There may be a few very large issues, but also a gazillion small factors that make up systemic discrimination, both racially and against women. It is impossible for minorities to fight those individually, especially not from a position of weakness. It is more effective to counter at least a small part of the net discriminative effect by relatively simple quotas.
And usually those policies don't make up the balance anyway.
Providing programs to help those in a weaker economic position more directly addresses the need, results in programs that everyone can feel that maybe they or their family might benefit from, and avoids perpetuating raced based discrimination and the resulting resentment.
If when economic equality isn't the inequality you're attempting to correct it's so highly correlated that it should be sufficient-- after all, a big part about why we care about the lasting effects of historic racism is that it has produced a lasting weakened economic standing.
A state government might have a very liberal or conservative party in power ... and a given policy might be considered the opposite, but they're not going to revisit it all the time.
The reasons for the policy too might have nothing to do with 'conservative' and 'liberal'.
Personally, I'm not really sure I buy into the idea that any given University has to have a given admissions policy and be 'liberal' or 'conservative'. There's room for a mix of policies across universities IMO / should be a mix.
Fankly I think you could tell most people any random policy is 'conservative' or 'liberal' and they'd just support or oppose it based on that label.
Definitions are all dorked up... and 'conservative' and 'liberal' is too weird and narrow a lens to view everything through.
Just as an example George W. Bush ran a campaign that very vocally opposed "nation building", it was thought to be a very important conservative value. George W. Bush then started the largest / longest nation building projects in Iraq and Afghanistan in decades ...
These terms often don't make any sense when applied.