That said, wrong opinions—which I am willing to state exist—do not deserve to be elevated, they do deserve scrutiny if stated.
Banning abortions is a wrong opinion. Perhaps some people have some reason to hold this opinion, and perhaps not all of these people are bigots (although many are). However they are still wrong. And when these wrong options are stated, they do deserve to be scrutinized, and they don’t deserve to be elevated in the general discourse.
However, your statement "banning abortions is a wrong opinion" is itself an opinion. Yet you stated it as if it's a scientific certainty, when in fact it's an opinion you don't share. My wife and I debate it all the time, and it comes down to a prioritization difference in my mind vs her mind. I prioritize the privacy and rights of the pregnant woman over the future existence of the fetus. She views the fetus identically to one that has exited the birth canal and is now a baby. She doesn't think there is a break in the continuum. I disagree with her entirely, but that doesn't make me right and her wrong. It just means that I put a higher priority on the woman's freedom than I do on the right of the fetus to develop into a human. It's amusing to me that when my wife and I argue about this topic, she is focused on the rights of the fetus, and I'm focused on the rights of the woman. We aren't having one argument over a woman's rights, we are having two arguments simultaneously. This is a nuanced view that the current political debate doesn't allow for. Her view was obviously influenced by walking into a hospital and watching parents pray by the side of incubators containing 26 week preemies, and then seeing activists debating whether third-trimester abortions should be banned. I certainly don't blame her for having that opinion when she has to reconcile those two ideas simultaneously. It's a lot easier to hold the opinion that you and I share when we view fetuses clinically rather than in incubators.
However I don’t see the statement “Women have rights to their bodies” as an unresolved political question. I see it as a pretty clear truth, as true as “slavery is wrong and should be illegal”. I have my reasons to believe this is so (which I won’t go into because we are debating whether “everything is political”, not abortion rights). So under my philosophical framework anti-abortion is a wrong opinion to have. And I am certainly not the only person to believe this.
My wife happens to be vehemently opposed to abortion, and also a woman of color. Yet you associated her with a bigot and climate change denial.
Which exposes similar thinking to what the OP was talking about: Not everything is political, but because my wife thinks differently from you on terminating fetuses due to her having worked in a neonatal ICU with premature babies, she's a bigot? Sounds like you are in a tribe and are lumping my wife into the opposing tribe based on one opinion she holds.
By the way, I find it ironic that your last sentence that condemns view points that differ from your own to be silenced and then mentions flat-earthers. The original flat-earthers gave Galileo the platform they thought he deserved: a life sentence in prison. They were confident and lacked the intellectual humility to believe opposing views should be countered, not suppressed. Ring a bell?