Should I ask my professor to change my project group?
I can give you some advice based on similar group dynamics I had.

While working in one of my thesis courses in industrial engineering/quality, I was paired up with a group that was fairly cohesive from the beginning. All, except one member, really made the effort to try on this project.

The one member, a gal, was not culturally and academically on the same page as us. I had her in a previous class and was known to cheat and probe for answers. It also showed she happened to be a bit crazy.

About a fourth of the way of our semester-long project, she went rouge and stopped showing up to our meetings, which in turn led to a lack of quality work, then a lack of work all-together. Come time for one of our presentations, we had clipped her powerpoint chart which had no meaning to our project and presented in front of the class. She immediately started presenting slides that weren't hers unannounced, obviously looking as if we were unprepared. We got an email, CC'ing the professor stating how we were "(explicit) this and (explicit) that for deleting her slide prior to the presentation." 

Rather than confronting the issue, we built a case, with screenshots, email threads, and evidence proving she was not contributing any work. Solution? Present the evidence to the professor and have them facilitate the discussion. Chances are they'll ask you to stick it out but may be lenient on grading you.

With the professor there, we were able to have the tough discussion and bring it up to them because chances are your group member's poor character has also rubbed off on the professor. You'd be surprised to find out what your professor is thinking. 

tl;dr version, come to your professor with concrete evidence on why this is happening, and see what options there are. The point of group projects in college are not to work with your friends, but rather be able to make difficult decisions with individuals you may not see eye to eye with. 

I"m positive after this experience, you'll be able to cope working with people you don't necessarily agree with, morally or otherwise. My recommendation, finish off the project with poise and build a case against your bad apples so they'll be barred from ruining another perfectly functional group project. 

Best of luck.