It's lawful to discriminate on the basis of religion unless there is a law that says it isn't
I'm sorry if that appears tautological, but it's a necessary point because many people assume, wrongly, that they are free to express their beliefs (religious or otherwise) and that other people are not allowed to discriminate in response. This is not true!
Stating that you don't like something someone said or did (or is) and refusing to deal with them as a result is an exercise in free speech and protected as such. Just as a Jewish person is free to make a public declaration of their faith (such as by starting correspondence with "B"H"), an anti-Semite is equally free to express their beliefs and discriminate against the aforementioned Jewish person. Freedom of expression means freedom to express morally, ethically, and socially reprehensible viewpoints.
The rights in the US Constitution (and similar rights in other jurisdictions) are limits on what the government can do, not what private individuals, including Stack Exchange Inc., can do.
Now, the government can, by legislation, extend such rights so they apply to private entities. Still, because such laws potentially infringe the free speech rights of those private entities, the laws are subject to the same sort of scrutiny as any other law that inhibits a right.
Can Stack Exchange Inc. limit it's users free speech?
They're not the government, so yes, they can. In general, a private organisation does not have to allow you to use their platform to express views, speak in a way, or at all if they don't want you to.
Unless, the way they do that is or amounts to unlawful discrimination.
Is there a law that makes it unlawful for Stack Exchange Inc. to religiously discriminate against its users?
Stack Exchange Inc. is headquartered in New York, so we'll assume that New York state law and Federal law as interpreted in the Second circuit is applicable. It may be that the law where the user is based might also apply but since that could be anywhere, we'll leave that for now.
AFAIK New York does not have a law that prohibits religious discrimination by a business against its clients.
There is a Federal law that prohibits religious discrimination for businesses that provide "public accommodation". So is an online forum-type website "public accommodation"?
Case law on this is subject to a three-way circuit split, but in the Second Circuit, the answer is yes; Stack Exchange Inc.'s sites are places of public accommodation, and they are not allowed to discriminate on the basis of religion.
Is banning taglines religious discrimination?
No.
It's worth quoting the rule:
Do not use signature, taglines, greetings, thanks, or other chitchat.
Every post you make is already “signed” with your standard user card, which links directly back to your user page. Your user page belongs to you, so fill it with information about your interests, links to stuff you’ve worked on, or whatever else you like!
Thanks and other statements of appreciation are unnecessary, and, like other chitchat, should not be included.
If you use signatures, taglines, greetings, thanks, or other chitchat, they will be removed to reduce noise in the questions and answers.
The reason for the prohibition is content neutral (all taglines are banned - not just ones affecting religious sentiments) and for a legitimate purpose (to "reduce noise"). Furthermore, they have provided a place to put "whatever else you like" that is automatically attached to all your posts. While it may affect and possibly upset some people who follow the Jewish faith, it is not discrimination on the basis of religion.
