You specifically used this phrasing:
proposing that a requirement on someone to disobey her religion
And I’m wondering about which part of her religion requires her to start a business. Which commandment is she “disobeying”?
If she lived in a Christian theocracy I’d assume her government would have different rules about discrimination but she doesn’t. She lives in a pluralistic society for which the government has legitimate interest in non-discriminatory business practices. They also have interest in not infringing on religious exercise but running a website business is not a religious exercise even if performed by a religious person.
What you seem to missing is that there is no requirement that any business deal with all customers within the supposed client base it represents.
You will not find durian in the produce section of any mainstream US supermarket. (You will sometimes find it in ethnic supermarkets.) Is that discrimination? No. Just because they sell produce doesn't mean they have any obligation to sell the produce you want. (Not that you do--if you don't know durian you do
not want to try it! Supposedly it tastes delicious--
if you can get past the smell. It is the only thing I ever knew my mother to not be willing to taste and she was normally very curious about food.)
Likewise, just because they make wedding websites doesn't mean they have to make same-sex wedding websites.