The so called religious rights bills sweeping some states are a reaction against civil rights laws that include LGBT people. Many of these states don't have civil rights laws, at the state level at least, that include LGBT people. Here in Washington State, we do have civil rights laws that include LGBT, but these laws specifically exempt churches and religious institutions. From what I understand, churches can still discriminate if they wish to under Washington State's fair housing and employment laws for GLBT.
Marriage Equality is a different issue. That Supreme Court ruling allows gay people to be legally married, but it doesn't require anyone to preform that duty; except for state employees such as county clerks acting on behalf of the state. If a church doesn't wish to preform a gay marriage, it's still allowed to make that choice.
Forcing someone to serve a gay marriage, such as baking a cake, is not part of gay marriage. It's more a function of anti discrimination laws, which many states don't have. Here in Washington State, we do have anti discrimination laws, but there are already exemptions written into those laws. The anti discrimination law doesn't apply to a church, but does apply, I guess, to a business, such as a bakery, as covered by civil rights laws. I guess that's what civil rights laws do. They tend to force people to not discriminate against minorities.
At least that's my understanding.
Here it's useful to contemplate what a libertarian might say. Libertarians who don't like coercion by government might oppose any civil rights bill that forces a business to hire or do business with someone they don't choose to do business with. This could apply to the issue of race as well. I'm not a libertarian, but thinking about what a libertarian might say can be useful in this discussion.