Basically I think what it's about is whether somebody can refuse somebody service or not at their business because somebody is gay. They're not claiming freedom of speech, they're claiming "religious liberty." I.e., these people think homosexuality is an abomination under God, therefore they risk divine wrath by serving gays in their restaurants and so forth. Nothing to do with the 1st Amendment, it's something more in lines with the 14th.
The principle disagreement with this is deeper though, it would seem to set a precedent that wouldn't just be about sexuality, but would apply equally to race, gender, or anything else. On the one hand I can see a point that my business is my business, and I should be able to refuse service to whoever I wish for whatever reason I wish. The libertarian in me agrees with that. On the other hand what comes to mind are the old pictures of "we don't serve blacks" and this kind of thing that so many people worked hard to end. While I'm a bit on the fence about all that generally speaking, I can't help but notice that all the laws that have been created to end discrimination in the private sector are rather meaningless if somebody can simply ignore them for, in the case of a religious person a religious reason, and in the case of a non-religious person (me for example) a moral objection.
The reason for the discrimination doesn't matter, it's still discrimination. As far as I know nobody has ever used the 1st Amendment argument you're using to try to overturn any anti-discrimination laws. If they were considered unconstitutional in fully developed arguments on issues of freedom of speech and discrimination, they'd have been struck down long ago. So I think the "hey, go read the 1st Amendment" argument may be a wee bit naive.
Like you said, we'll see how this plays out in court probably. Thanks to the 14th Amendment the government has never been allowed to do this kind of thing, but I don't know how it plays out in the private sector. Refusing to hire somebody because of their race, gender, or sexual orientation is discrimination and illegal, plain and simple. You can't even ask somebody during a job interview if they're married or not.