Talk Elections

It might seem like a weird question to ask, but the political coalitions have changed quite a lot since Casey passed away in 2000. I personally think he would be a Republican, I just can't see someone as staunchly opposed to Abortion as Casey was still being a Democrat.

Democrat if for no other reason but to help his son out.

He would still be a communitarian Democrat.

Probably Democrat. He may of been a conservative on Abortion and other civil issues however that would not necessary make him a Republican. From what i can find i think he could just quite as well be a Social Moderate-Conservative and Fiscal Liberal-Moderate Democrat and could find a home with similar democrats like the Blue Dogs.
Here is from Wikipedia below on his Fiscal Policy in Pennsylvania. Dont think it is quite what a republican would do:

"Casey brought what he called an "activist government" to Pennsylvania, expanding health care services for women, introducing reforms to the state's welfare system, and introducing an insurance program for uninsured children (which became a model for the successful SCHIP program later adopted nationwide). House Bill 20, entitled the Children's Health Insurance Act, created the Children's Health Insurance Program (CHIP) in Pennsylvania. According to PA's CHIP website, "Pennsylvania's CHIP program would later be used as the model for the federal government's SCHIP program. Legislation for the federal CHIP program was signed into law August 5, 1997 by former President Bill Clinton." ".

Democrat.  And he didn't like Clinton, so it would be interesting to see who he would have supported in 2016.

Assuming he's not willing to compromise on abortion or economics...

Either a Democrat with a failed political career or an independent who never runs.

Casey was, I believe, asked multiple times to defect, and refused. I imagine it would be much the same today.

I think people really overrate how often people change parties.  If you weren't deathly afraid of your own re-election and survival as a member of the Democratic Party going forward, there is no reason to switch.  Ideology isn't even the main factor, you picked a "team."

Even though he was staunchly pro-life, his other positions are still within the mainstream of the modern Democratic party, so he'd most definitely be a Democrat.