I was born a male, but I have a female identity and name due to psychological dispositions. I also have no sexual feelings for men or women and I do not like romantic intimacy. There is no Shi'a that would be willing to accept me due to my psychological, sexual and romantic dispositions. But the only people interested to be my partner are non-Muslims that are not pious or religious.

Is there any blame upon me for vowing not to marry anyone unless they're Shi'a? Even if that means I don't marry for the rest of my life? Would marrying a non-Muslims who is irreligious be accepted? I know that Shi'ism stresses marriage, so I don't know if I have to be married, even if that means marrying a non-religious person.

There is no sin if you stay unmarried. Just make sure that you do not commit any haram sexual acts. If you can guarantee that, then you can stay unmarried. Also, it would not be permissible to marry those non-Muslims who are willing to marry you. So there is no blame on you if you stay this way.