I am strictly asking about whether the First Amendment protections of religious freedom will apply to those Christian groups that declare homosexuality to be sin and thus do not recognize gay marriage etc.
Not exactly sure what you mean here. They will likely be forced to allow a gay persons partner benefits of a spouse. But that is about it.
How will the govermnent treat these groups?
Luckily we have a history lesson to look at. How churches were treated after interracial marriage became legal and banning them was illegal.
No church was forced to marry any interracial couple.
Will they lose access to public institutions or settings?
Just because they wouldn't marry a same sex couple? No. However, if they discriminate against gays or other such things, they could lose public funding.
Will they lose their tax exempt status?
There are many ways they could lose a tax exempt status. If they openly support an anti-gay political candidate. If they run a school that does not allow gay children or children of gay parents. But if you are wondering if they would lose their tax exempt status because of not performing ceremonies for same sex people, that is not going to happen.
Will they be seen as a cultural pariah?
What do you think of a church in nowhere alabama that would not marry a white and a black couple (one man and one woman)? Or a white guy and an asian girl? Would you think that they are losers?
The church will have to live by what it does. Yes, in time gay marriage will be allowed everywhere in this country. Within a short time after that, people will wonder who the heck the dumbasses are who opposed it. That is the way it goes.
Will they be considered guilty of "hate speech"?
Why? What do they say? Kill gays?
Is there a way that groups that oppose homosexuatity on religious grounds will be able to be accepted in the New America, or will this be the wedge issue that finally delegitimizes religion in the public square (or alters it forever)?
This whole post is rather ridiculous.
First, the fundamentals are getting less legit every day. When they get up and say that evolution is just a theory, when they say that this is a christian nation, when they say that intelligent design should be taught in school, when they say the earth is 6500 years old, they are driving a wedge that separates them from legitimacy.
Their views are opposing gay marriage are just another pimple on an already awful face of their faith.
The real question is whether as science figures more and more stuff out, does this drive religion out of the picture?
People no longer look at the tides and believe that they are miracles because they can't explain them any other way. When there is less and less need for the saying, "I don't know, God did it".
Your questions are really ridiculous. If a religion preaches racist, bigoted, or other ridiculous beliefs, you don't think they should be viewed as being racist, bigoted or stupid? That for some reason their religious belief should excuse this stupidity?
Sorry. That is not the case. You are what you believe in. If your religion teaches racism, and you believe that, you are a racist.
Religion is not some neat little excuse that allows you to be a prick to the rest of the world.
Religion is less and less important in society. That is just the way it is. Religion will either become more or less important in society by its own merits.
But if you are wondering if churches will be able to decline marrying two guys because in their views, though God made them Gay he doesn't want them to be married to someone that he made them attracted to, then they would not be forced by the government to do so.
Just like the government would not force a church to marry a white guy and a black girl.
What the rest of the country thinks about them is kinda up to the rest of the country, don't you think?