It's trivially easy to create a consistent belief system. Simply have no beliefs. The mutually exclusive properties are consistency and completeness (although t

It's trivially easy to create a consistent belief system. Simply have no beliefs. The mutually exclusive properties are consistency and completeness (although these can be mutually satisfied in certain limited circumstances not likely to be relevant here). You can have no belief at all about abortion. In that case, you are free to choose one as an axiom, although you are also free to not choose. If you choose a belief about abortion as an axiom and the result is that you end up believing both a thing and its negation, then you will need to abandon one of the necessary premises for that construction.