Why have Americans gotten more liberal on most social issues, but are largely unchanged on abortion rights?

God says, "Do not shed innocent blood."

God says, "Man shall not lie with man as with womankind; it is an abomination."

These are real problems among the American people who hold to Judeo/Christian values from our forefathers.  God never says "Let's make a deal;" He always says, "This is the deal."  God doesn't change.  Bible says, "What has been, will be."  "There is nothing new under the sun."

Sin is still sin whether liberal, conservative, Democrat or Republican.

Why should anyone decide that only men & women should marry? If there's 2 consenting adults why should it be anybody's business what they do in private or what gender or nonbinary gender they associate with. Why are these anybody's business. What's wrong with us accepting that there are different people in this world and to ask that we respect those we don't understand?

Why is it right for Conservatives to expect everybody to conform to their rigid point of views when we don't care? Just leave people alone. What we do mind is when someone is being a bigot and being disrespectful based on race, genre, or sexual orientation.

No one would argue with Cons if Cons kept their bigoted thoughts to themselves. They're the ones who start fights by making ignorant statements like Santa Claus can only be white. It's an imaginary character. Who cares? Or Jesus can only be represented as white. It's dumb comments and inaccurate comments like this where when people are being stupid they'll be called on it. They can whine and cry about it all they want and try to deflect but that doesn't stop them from being the person who started the fight. IF white supremacists don't want to see POCs represent Jesus they don't have to watch it, they don't want to intermix with POCs they can live in their homogenous suburbs and be left alone. 

Abortions in the medical field will define the development as just a cluster of cells until it reaches a certain development. There's a more logical explanation for that. No one is every going to want to abort a fully developed fetus unless something went terribly wrong and maybe the baby won't have a chance at living. Rather than forcing the birth it's more humane to abort it. These are incredibly personal decisions and it's very invasive for the government to intervene and force people to have babies when the development can be prevented. 

At the end of the day, we don't want people want Conservatives to micromanage and dictate extremely personal decisions that people would have the freedom to make themselves.

That being said there has been a growing number of Conservatives in favor of pro-choice. Tomi Lahren got her show plugged/canceled on Fox because she voiced her opinion for being in favor of pro-choice. A woman's right to choose what she wants to do with her body. I don't actually the support for pro-life covers all Conservatives because there are Conservative women who came forward to voice their opinion to say they support a woman's right to choose what they want to do with their bodies. It's highly powerful religious people who want to mix religious beliefs and government together. They're a minority but very powerful.

A woman's right to regulate her own fertility can never be interfered with. The bigot Evangelicals and ardent supporters of the former president want to dominate women and it is not happening.  Have a good look at the V.P. The future U.S. president. 

call it what it is-- there is no sucjh thing as murder rights.

same people who support abortions, used to have no problem with slavery

The percentage of people who are willing to support abortion has grown as the loudness of the opposition has grown - so that it seems we (Americans) are making no progress.  Methinks you are not looking closely enough at the trends.