Consider a software that allows users to create profiles that identify the user. If this software includes and allows users to choose what god/deity they believe in (or their favorite god/deity), is this legal?
Under the First Amendment, "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof". Consequently, there can be no government action requiring the expression of beliefs of a particular religion, nor prohibiting such expressions – or, requiring or prohibiting expression of a general belief or disbelief in religions as a whole. This neutrality requirement holds only of governments, therefor a person can in his dealings with others require or prohibit expression of a religious viewpoint to the extent that they can make such a (non)expression a pre-condition for such dealings. Such dealings can be purely social, or they can be financial.
However, there are currently some limitations arising from commercial dealings and the Commerce Clause of the Constitution, which allows Congress to regulate business. For example, Title VII of the Civil Rights Act of 1964 prohibits discrimination against employees based on religion. This limits an employer's right to religious expression, for example if they announce that Pastafarians need not apply. Title VII only addresses employment. Title II has an analogous prohibition against consideration of religion in "public accommodations" (theaters, hotels, restaurants...). The Fair Housing Act similarly prohibits religious discrimination in housing.
We need not get into the question of whether prohibitions against religious discrimination contravene the First Amendment. Until SCOTUS or Congress says otherwise, there are specific narrow limits on one's First Amendment rights w.r.t. religion. There is no software anti-discrimination law, so no basis for thinking about the question in terms of anti-discrimination laws. In lieu of a law that addresses religion and software, you may express your religious or non-religious views in software as you please.
Insofar as all anti-discrimination law are based on the premise "You may not consider X in making decisions", and setting X to be "religion", an anti-discrimination law applied to software would at most prohibit the prohibition of a religious expression, that is, would make it illegal to prevent a customer from making a religious expression within the scope of the software. A law which required software to suppress religious expression would be a maximal contravention of the First Amendment. So it is legal to allow a user to use the FSM as his avatar.