The problem that arises when you say that businesses can't operate according to their religious beliefs is that it doesn't make the problem go away. All it does is shift the moral decision to the govt, and de facto makes them operate like a church - a violation of separation of church and state - while it also doesn't eliminate the inconsistencies and inequality, despite claiming otherwise.
For example - why do gays get to marry and not polygamists? Where's the equality? The govt says one is legal and the other not, yet the very base principle of allowing gays to marry and not just heterosexuals is 'equality'. Yet that equality is very selective to what the govt considers as protected groups, which doesn't apply to all. In other words, the govt plays moral arbiter and religious institution.
Now throw in the 'identity' movement. If you can identify for example what 'gender' you are, why can't the principle of 'identity' be equally applied? Why can't I identify as a cat, and demand litter boxes in all public restrooms? Or why can't I identify as 'transgenerational' and have sexual relationships with minors? Or transracial? Or transpecies, and declare myself a separate species superior to other humans? Or simply not human at all, and not beholden to any laws?
Of course these won't happen, because the govt will pick and choose. It denies these rights to citizens according to religious belief, but yet feels free to play moral arbiter based on 'equality.' Yet they apply it wholly unequally and in a completely hypocritical manner while actually merging church and state, while claiming to separate it.
It's nothing but a total scam and simply gives the govt more power (as a religious institution no less) in the name of 'equality.'