You can read it here.
Christian, and other religious, philosophers who maintain traditional views on the intrinsic purpose of human sexuality would do well not to publish or defend their views in print or at conferences until they have received tenure.
What this petition reveals is that there are many in our profession who are willing to employ their clout to punish institutions that, and by extension individual religious philosophers who, will not acquiesce to their disputed views on human sexuality and the nature of the human person. Apparently, many in the APA want to declare, without discussion, debate, or serious reflection, one question of philosophical anthropology forever settled and off limits.
According to the petition, and the APA provision it cites, a religious institution may hold certain religious beliefs about human sexuality, but it may not conduct its business as if those beliefs are true. I am at a loss to see how this is consistent with any serious and substantive understanding of religious liberty. It seems, then, that for the signatories, consenting adult citizens who build and establish academic institutions within the confines of deep and sophisticated religious traditions, can never in principle trump the interests of consenting adult citizens who engage in particular sexual practices. This means, of course, that philosophers employed at Christian institutions ought not to be terminated for any sexual act done in private with a consenting adult. If, for example, Baylor University were to discover that one of its married faculty members was committing adultery with another married faculty member, it ought not to act on its Christian beliefs without provoking judgment on the part of the petition's signatories. So, according to this petition, Christian institutions are morally required to act as if their beliefs are false, even if these institutions, its founders, its members, and its constituencies all believe they have good reason to believe that their beliefs are true.
In the name of standing against discrimination based on sexual orientation, this group of philosophers is demanding that the APA discriminate against institutions that do not embrace one particular, and far from established, view of sexual orientation and human sexuality.
The persecution of serious Christians is no longer a "slow train coming," to quote Bob Dylan, it is picking up speed.