I can’t speak to healthcare generally but one of my college roommates was from China and she just could not wrap her head around the politicization of birth control in the US. I remember her asking us if Americans thought it was dangerous or addictive because she couldn’t understand why it was so controversial that the affordable care act required birth control to be covered.
A sibling comment has already mentioned the one-child issue, but I wanted to say... Chinese culture is so deeply different from American culture about all sorts of things about reproduction and fertility.
Chinese people's attitudes toward the one-child policy and also sex-selective abortion are complicated and varied, but they don't seem very similar to Americans' attitudes at all!
In the U.S. it's common for people's religions to completely formally proscribe some forms of birth control and/or abortion. This has led to a big political debate about what the scope of their legal rights to avoid subsidizing these things for other people should be. It's not surprising that that debate should exist, but also not surprising that it would be uncommon in China where (1) the most practiced religions largely don't have these teachings and (2) people don't have a common expectation that the state will give their religious practices and beliefs a considerable amount of deference.
I think a median American attitude is that nobody else should pressure you to have more or fewer children than you want to; if your religion encourages you to have children, other people are also largely supposed to respect that, and in modern times, if you just don't want children, other people are also largely supposed to respect that. (In blue tribe environments having many children is suspicious and in red tribe environments having no children is suspicious, but in both cases people are increasingly effective at pushing back socially against other people's scrutiny about this, and even at pushing back against their own families' judgments or preferences.) (These considerations don't necessarily apply the same way outside of opposite-sex monogamous married couples.)
I don't think these norms are common in the same way in China or in Chinese cultures elsewhere. In particular, I think even if Chinese people don't all think their parents, or governments, should get to decide how many children they have, it doesn't seem like many will reach U.S. levels of offense that prospective childbearing couples' parents, or governments, have an expressed preference and actively try to influence this.
The PRC perspective on birth control, specifically, is unique, since the CCP forced birth control and abortion on its population for decades as part of the "one child" policy.[0]