What do political parties and other groups think should be done about the issue with women's rights and the church?

That would depend on the religion involved. In the United States of America, the Government has no business interfering with religious dogma, tradition and issues.

Politics should not and legally can not be involved with this issue. People within these parties may have an opinion, but legally the parties should not be involved. Separation between church and state was originally setup to prevent politics from being involved with these issues, not to prevent the church from interfering with politics.

Thomas Jefferson made the issue very clear by explaining the wall of separation that the state should never tear down. The issue has always been that the government should not get involved with the church.