The problem arises when a given practice, such as abortion impacts a third person. While there are those who say that an unborn child does not count as a person, others perceive that it becomes a person at conception. If you take the second position, preventing a woman from having an abortion is perfectly reasonable, except in such cases where it is necessary to sacrifice one in order to save the other. (Very, very few pro-life people would dispute the right of a woman to terminate a pregnancy where there is a clear and present danger to the life of the mother.)
(Edited to fix typo)
While very few “pro-life” proponents would deny a women abortive care in a life threatening situation, most support laws that, in practice, reduce or deny proper healthcare to women in life threatening situations.
I think it's the terrible logic that ruins this sentiment. Very few of us would extend his logic to beating one's spouse, that is, "my religion prevents me from beating my spouse so I don't, but I won't impose my morality on others." So, we have there be laws that arrest and jail abusers.
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(Edited to fix typo)