Whatever you might think of the various professions... As long as it is legal, it seems the major payment service providers should not pass on their moral code onto everybody else. What's next? You get no water/power/whatever if you run a business that the service providers simply do not agree with?
But your general question is an open debate. If you run a hosting company do you have to host things you disagree with? If you run a transaction company doy you have to exchange with parties you disagree with? What if a certain type of transaction is too high risk, do they have to do it anyways?
Personally I'd like to see things lean more towards being agnostic to avoid amplification of the popular opinion but it isn't a cut and dry topic without corner cases or hard to define regulations.