Answering the question, I think it definitely can be made legal (even though it should be possible). The problem are the Freedom of Religion laws like Indiana has and that I'm sure Pence would like to take national. Although it's been most widely covered in LGBT discrimination, that law really applies to anything that might infringe on someone's religion. Technically what the law says is that an individual/business/church can discriminate and then use the law as defense if they think that the actions are a significant burden on exercising their religion. So really it could apply to many things beyond just LGBT topics. A Christian could for example refuse service to a Muslim, or Atheist, or vice-versa, and use the law as defense that it is a burden to serve a non-believer. That's pretty much the definition of discrimination in my book.
Thankfully it's only a law in Indiana I believe currently. It was attempted in Arizona and didn't pass. So at least at that 1 state level it can be done. I'd bet more hard conservative majority states will try to pass something similar. Personally I don't see how the law doesn't conflict with other non-discrimination federal laws, but maybe that's something for the Supreme Court to decide.