I came across this blog post recently, which responds to the RFRA ("right to discriminate") bill in Indiana. The point is correct (despite the unhelpful headline), but the examples are hard to take as valid examples because they mostly focus on the Old Testament. I get why the post would focus on books like Leviticus and Deuteronomy, as many Christians arguing against homosexuality seem to hover on these books, but Christians do not view things through a monolithic lens.
1) don't accept the OT as God's Word (it's merely for informational purposes only);2) realize the context of ceremonial laws for Jews but still accept the OT as part of Scripture, or;3) pick and choose verses à la carte to back up an argument they could probably better make from the New Testament. This is why silly arguments crop up about clothing of mixed threads, eating shrimp, and trading daughters for goats. The OT and NT are wholly different cultures, and the texts are written with different purposes.
In short, not all books in the bible can be interpreted or applied using the same "lens", as they are NOT all the same exegetically. Leviticus concerns laws for Levites and the Jewish people, mostly for ceremonial practices; Psalms is poetry; Kings is Historical; etc.
If you're going to argue against gay marriage or homosexuality at all, Leviticus is not the book to do it from. That particular application forced upon that particular verse for the particular purpose of winning a particular argument therefore puts the rest of the book out of context, particularly for modern application, but, whatever...
Regardless of one's position of this issue, the morality of homosexuality is not the true point of this particular issue. The belief that one should refuse service to a customer who sins is not only NOT commanded of Christians, it's highly illogical and impossible to follow. For those who see homosexuality as a sin, it is hardly the only sin, or even the "worst" of sins.
Using examples from the New Testament, Christian business owners couldn't serve the following:
Now the works of the flesh are obvious: sexual immorality, moral impurity, promiscuity, idolatry, sorcery, hatreds, strife, jealousy, outbursts of anger, selfish ambitions, dissensions, factions, envy, drunkenness, carousing, and anything similar. I tell you about these things in advance—as I told you before—that those who practice such things will not inherit the kingdom of God.
And this one example only encompasses all of three verses - Galatians 5:19-21. Not to mention some of these things are vague terms to us that would not have been vague to the first readers. What is "moral impurity"? To me, that could pretty much be the only word needed in that list. Wouldn't it cover everything else? Why list it separately? The others aren't even items to clarify "moral impurity". It is a singularly isolated item within the total list.
And dissensions? Hooo-boy! Dissension to whom? Jesus? Each other? The Government? The Church? All of the above? If all, then I think everyone is in trouble. I guess none of us can have cake... Unless, you know, the Queen demands it by shouting, "Let them eat cake!" or something like that .
Look, the point is this, how could you even possibly enforce this? It would only work with people you know or is noticeably one of these things or who has admitted one of these things. And, the above verse states a list of items as sins, it doesn't say to refuse service to those who've committed those sins, or any sin. Which, if it did, you'd have to close up shop because Romans 3:10-12 states there is no one who is righteous, no one who does good. And that is because, skipping down to v23, All have sinned. We are all sinners. And, we have all fallen short of the glory of God.
Christian bakers couldn't even bake themselves a cake if they want to make sure they don't condone sin by serving sinners.... This is what would have to happen to even just "avoid the appearance of evil" (1 Thessalonians 5:22) and this would only continue to misinterpret and misapply this verse, as many do today. "Avoid, stay away from, etc..." - In other words, don't do these things yourself.
Here is what the New Testament does teach: Preach the Gospel (Mark 16:15), let people know why Christ died for them and how they can be saved, should they want to be (1 Peter 3:15). But, if they've asked and you've told them and they don't want it or they reject it, that is their choice. Move on! Your part is done (Matthew 10:14). At that point, spend time "working out your own salvation with fear and trembling" (Philippians 2:12) and maybe worry less about what others outside the faith are doing (1 Corinthians 5:12-13) !
The RFRA is therefore pointless, meaningless, and unproductive. The same goes of boycotts. Same thing, but flip side... reversing the claim that Christians shouldn't go to businesses that have owners or managers who sin or allow employees or others to sin. That is just as pointless, meaningless, and unproductive. Both hurt the Christian mission to evangelize and demonstrate the teachings of Christ to others. If you are Evangelical, this bill (and boycotting) is the very anti-thesis of your mission to evangelize.
 Which, actually, never happened either. Jean-Jacques Rousseau originally said it about an unnamed "great princess", who is probably a fictional character and not referenced as an historical figure.
 In the case of 1 Corinthians 5, it is a specific case about incest that was happening between church members. Paul clarified that they were immoral and to expel those people from the church. He went on to say that the Church should not associate with sinners like these, but note he clarified other Christians who are flagrantly sinning, not anyone outside the church, "or you'd have to leave the world completely." Since we can't leave the world completely, things like the RFRA seek to force the world to just be more like us because we want to judge those outside the church as well. And, this is exactly what Paul said was none of his business and therefore should be none of our business either! This does not mean Christians cannot or should not be a part of society or culture at large, but our "jurisdiction", of sorts, only seems to be from within.
Also, "associate" is not exactly the same as "avoid" or "shun" within the English language, but I would need to do a word study of the Greek to figure out what might have been intended because many think of "excommunicate" as kicking out and refusing any contact whatsoever. If the person repents, they are welcomed back in. I would imagine though that associate means not to engage in the same behavior or condone the behavior of a fellow Christian.
Update: see Part II for the flip side to this coin. Should RFRA Opponents "Boycott Indiana"?