In the US, those issues are handled through court cases, regardless of where public opinion stands. For example, elective abortions (without health risks or something else) in the second trimester or later is very unpopular in the US and the EU. Only about a quarter of people think it should be generally legal after the first trimester: https://news.gallup.com/poll/235469/trimesters-key-abortion-.... That matches up with the law in most of the EU, where the limit for elective abortions is 10-14 weeks. (As I recall, the UK is the exception at 24 weeks.)
The US constitution doesn’t say anything about abortion, or anything that could really be construed to be about abortion, but the Supreme Court has interpreted it to protect abortion up to viability, usually 22-24 weeks. So the Supreme Court has interpreted the constitution, which says nothing about abortion, to create an abortion right so broad France or Germany’s or Denmark’s abortion laws would be invalid in the US.
The topping on that cake is that the US is that the US is the most religious developed country in the world, more so than countries like Poland.
Which is why Supreme Court appointments get so heated here.
https://news.gallup.com/poll/117328/marriage.aspx
Here's polling on interracial marriage:
https://news.gallup.com/poll/163697/approve-marriage-blacks-...
Interracial marriage became legal nationwide in 1967 with Loving v Virginia, but wasn't approved of by the majority of Americans until 1997.
Edit: I only add this to support the the comment replied to.
It's certainly different from state to state.
Most cases that reach the US Supreme Court aren't about whether X is good or bad (let's say X is abortion or gay marriage) but whether X is so good that the Federal government should compel states to allow it, or so bad that it should compel states to forbid it.
No, most of them aren’t about good or bad, which is a policy judgement generally reserved for the political branches, at all.
Its about whether X or Y is consistent with the law (including, as the paramount law, the Constitution of the United States.)
If “it seems right” is a good way to run a country, why do we even have laws?
I don’t think abusing silence and substantial ambiguity is a coherent approach to legislation. If something important in the law is ambiguous, the correct approach in my view is to make it unambiguous by the usual legislative process.