The assertions themselves are so unbelievably vague that they could easily go either way with cherry-picked polling. Most people support abortion in cases of rape, so if you do a poll asking if people think some abortion should be legal, you will easily get a majority. If you ask about easy access to abortion in the 9th month, you get far lower levels of support. Saying "most support legal abortions" is practically meaningless without specifying what type of abortion they support.
The other two depend very much on how you ask the question. It’s nowhere near as simple as you make out.
Getting the most votes isn't what translates to forming a government in the US. The big things are: having your family members run state governments, setting district lines, and setting up laws to prevent people that disagree with you from voting. Not to mention just having a lot of money to bribe already elected politicians.
Anti-voting regulations, while frankly absolutely despicable, I've not yet seen any studies regarding a significant effect. Do you have any data on that?
Add to that the fact that many voters are single issue voters, so their opinions on different policies don’t end up amounting to much.
So even if some policies are popular overall, they need to be popular enough to overcome these things to form a durable coalition that advocates for them in the halls of power.
Anti-Abortion: about or above sixty percent of Americans support legal abortions
Climate change: two thirds of Americans view it as a top priority and that the benefits of action outweigh the costs
Guns: sixty percent to two-thirds of Americans support stricter gun control. 90–92% support mandatory background checks
Taxing Wealthy: again, sixty percent to two thirds support higher taxes on the wealthy.
Those are the pillars. Those are the core propositions.
Americans do not support them or not by a margin of 1.1%