There are many possible thesis statements for this subject because there are many aspects of this issue that you could look at. Here are two possibilities.
One thing to look at would be the question of when and why abortion became such a big political issue. I would argue that it only became an issue after the Supreme Court handed down its ruling in Roe v. Wade in 1973. Before that, abortion had not been a major political issue even though there had been a number of states where abortion was available in many circumstances. After that, pro-life forces came to believe that they needed to mobilize. My thesis statement here would be something like “Even though abortion was legal in many states before Roe v. Wade, there was no conservative push for anything like an anti-abortion amendment to the Constitution. It was only after Roe that the pro-life movement became energized.”
Another thing to look at would be the demographics of public opinion on this issue. Different groups of people have different opinion on the issue. For example, younger people are more pro-choice and older people are more pro-life. Overall, white people are more pro-choice and people who are not white are more likely to be pro-life. Educated people are more likely to be pro-choice than people with less education. You might look at more of these differences and try to decide why you think that the various groups have these opinions. My thesis statement here would be something like “In the US today, different demographic groups have different opinions on abortion. In this paper, I will explore these differences and propose reasons for them.” You should note that some teachers do not like thesis statements like this that do not take a position on the issue. I allow my students to write such thesis statements, but some teachers do not.
Either of these would be a good thesis statement (at least in my view) on the politics of abortion.