You do that a lot here...say that something is Catholic when it is not...you use the sins or just lack of knowledge of Catholics to define Catholic doctrine, which is obviously insane, not to mention disingenuous. You should stop doing that. Make your positions stand on their own. Don't use Catholicism to support something that is not Catholic.
Now, as to what we should do in a pluralistic democratic republic...
Laws properly address consequential morality (which is primarily secular, albeit with religious overlap): Abortion is as much of a religious issue as burglary, theft, assault and murder. These are sins, but they are also crimes because there are victims. We don't outlaw them because they are sins. We outlaw them because there are victims. No one thinks laws that protect victims are forcing religion on other people. Disagreement by religions about abortion should be entirely irrelevant to abortion laws, since this is not a religions issue. It is a protection of victims issue...the primary function of government.
Laws should not address non-consequential morality (which is purely religious):Abortion is not a religious issue like contraception is a religious issue. In contraception, there is no victim. With successful contraception, no conception occurs, so there is no victim. Passing laws to force religion like that on people is wrong, and I would vote against that as a violation of the 1st Amendment.
I believe the Church in all things. I don't enforce my religion on anyone. I do support laws which protect victims.