2 very different things imo. One is clear instances of racism. If a cake shop is objecting to making an LGBT wedding cake on religious grounds, I don't think it is right to force them to make the cake, that violates the owner's religious rights. The same goes with trying to force a conservative Christian pastor or priest to be the officiator at an LGBT wedding.
The bible pretty clearly speaks against LGBT stuff in several places (Leviticus 18:22, Leviticus 20:13, Romans 1:25-28, 1 Corinthians 6:9-10, 1 Timothy 1:10, Deuteronomy 22:5, among others), so many Christians just don't feel comfortable having any degree of participation in an LGBT wedding. Believe it or not, most Christians don't have hate in their hearts for LGBT people, we love all people just as God commanded us to and many Christian churches have no issue with LGBT people attending, but at the same time we can't really deny what the Bible says about LGBT stuff; if it is a sin as it seems to be, we ourselves would be participating in sin if we took any part in an LGBT wedding. As a Christian myself, I'm not against LGBT marriage, if they want to do it and risk sinning, that is between them and God in my eyes, none of my business. I just wouldn't feel comfortable participating in an LGBT wedding myself, as anything more than a simple guest maybe. I also have no issues with being friends with LGBT people, and have several LGBT friends and acquaintances.
Didn't answer the question. They are not different things at all, they are the exact same thing. Refusing to sell a cake based on beliefs. The only potential difference is that one person claims their beliefs are religious, but perhaps they are lying, or perhaps the other person also cites religious beliefs. To my knowledge (I am no biblical scholar), there is nothing in the bible that is against interracial marriage. In fact, I'm pretty sure that the Bible speaks in favor of it in several places. Some verses that seem to be against interracial marriage are actually against interfaith marriage, and those verses are mainly in the old Testament. The new Testament seems to speak in favor of interracial marriage, as long as the other person is a Christian. So, I'm not sure that a Christian cake shop would have much of a leg to stand on claiming religious beliefs as a reason for not making a cake for an interracial marriage.
If you don't want to bake a cake for a gay couple because you're uncomfortable because of the bible, and I don't want to because I think gay people are icky, is it ok for you not for me? Is discrimination ok if it's religious? I'd say that one is a clear instance of religious rights, while the other is simply an instance of being bigoted. Thinking that gay people "are icky" doesn't feel like a valid reason to deny an LGBT customer, it just feels bigoted and wrong. On the other hand if you feel like you would be sinning in the eyes of the Lord if you participated in an LGBT wedding by making the wedding cake, I don't feel like it would be right for the Government to force you to Sin, especially when there are plenty of other cake shops out there that the LGBT customer could go to.
The only way requiring a baker to sell a cake is a violation of freedom of religion is if you argue that selling a cake to a gay couple implies acceptance or support of gay marriage. Then why wouldn't forcing me to sell a cake to a gay couple also be endorsing gay marriage, and therefore be a violation of my freedom of speech? I suppose in a way it would
Can a baker refuse to sell a wedding cake for a second marriage or an interfaith marriage? There is strong biblical arguments against both of these things. So, a baker can refuse on these grounds as well I presume? I suppose so. You are correct that their are biblical arguments against both, so I suppose that if a baker didn't feel comfortable making a cake for an interfaith or second marriage because he felt like he would be participating in sin, it would be wrong for the government to force him to make the cake, just the same as it would be wrong for the government to force it for an LGBT wedding.
But, why do the bible verses matter? If I thought god opposed gay marriage but didn't have any bible verses to support that, would that then not be ok? If we require a biblical or otherwise scriptural argument, or require that a view is couched in a mainstream religion, then that is a clear violation of the establishment clause. I feel like you need some sources if you are going to claim that something is wrong on religious grounds. I don't think it would be ok to claim that God is against something when you have nothing but your own word to back it up. If that was the case, God's name could be used to commit many evils (as has been done in the past).
So then, lets say I believe that interracial relationships are sinful and opposed by god. Furthermore, I believe that black people are actually a race created by the devil to taint humanity, and to serve them at all is offensive to god. I deny service to any black person and refuse to sell any baked goods to an interracial couple based on these beliefs. Are you ok with that? Negatory. Like I said above, I think you need sources if you are going to claim religious beliefs as a reason for doing or not doing something. You can't just make up your own religion as an excuse to hide your own bigotry, too much potential for abuse.
If not, suppose that I took a polygraph test that indicates that I sincerely believe these things. Is it ok now? They would still be your personal beliefs, if you can't back them up with sources from a Holy book, I don't really think you would have a leg to stand on. Same goes for other religions besides Christianity, I don't feel like it would be right for the government to force anybody to do something that is against their own religious beliefs, as long as it is an established religion and not just something that somebody made up. I think it would be just as wrong to force a Hindu person to eat beef or a Jew to eat pork, as it would be to force a Christian to make an LGBT wedding cake if they felt like they would be in Sin if they participated in an LGBT wedding by making the cake.