"
church offers no absolution
She tells me
The last line, "My church offers no absolution" is continued on in this line, with his partner expressing that he should "worship" them in the bedroom - which is an euphemism for sex. The sex is clearly meant to be a substitute for baptism in this case.
"I should've worshiped her sooner" conveys his disappointment for not finding acceptance for who he was sooner, and the "We were born sick" expresses his self-judgment and ambivalent emotions upon his homosexuality growing up.
The other lines, "If the Heavens ever did speak / She is the true mouthpiece" support the idea that his religion is standing in his way, that he realizes that he should have accepted his feelings for his lover sooner, but that, growing up, it wasn't that easy.