He had reached the open backdoor of All Hallows. Stepping into the porch he doffed his hat, took the card from his pocket and tucked it again behind the leather headband. Damn it. I might have tried to work M’Coy for a pass to Mullingar.

Same notice on the door. Sermon by the very reverend John Conmee S.J. on saint Peter Claver S.J. and the African Mission. Prayers for the conversion of Gladstone they had too when he was almost unconscious. The protestants are the same. Convert Dr William J. Walsh D.D. to the true religion. Save China’s millions. Wonder how they explain it to the heathen Chinee. Prefer an ounce of opium. Celestials. Rank heresy for them. Buddha their god lying on his side in the museum. Taking it easy with hand under his cheek. Josssticks burning. Not like Ecce Homo. Crown of thorns and cross. Clever idea Saint Patrick the shamrock. Chopsticks? Conmee: Martin Cunningham knows him: distinguishedlooking. Sorry I didn’t work him about getting Molly into the choir instead of that Father Farley who looked a fool but wasn’t. They’re taught that. He’s not going out in bluey specs with the sweat rolling off him to baptise blacks, is he? The glasses would take their fancy, flashing. Like to see them sitting round in a ring with blub lips, entranced, listening. Still life. Lap it up like milk, I suppose.

The cold smell of sacred stone called him. He trod the worn steps, pushed the swingdoor and entered softly by the rere.

annotation:

I spent some time digging into what Bloom means by “a pass to Mullingar”. Mullingar according to Wikipedia “is the county town of County Westmeath in Ireland.” further reading revealed that Joyce himself spent some time there as a child and it appears 16 times in his novels and 12 times in Ulysses alone. ( source ) I’m not sure, however what he means by searching out M’Coy for a pass there. Mullingar is a popular town and has quite a few events covering all kinds of sports, but I don’t know why M’Coy would have some special access to any of them considering that he’s an assistant to the coroner in Dublin. The main attraction seems to be the church, Cathedral Of Christ the King ( wiki ) which seems to make the most sense as a reference since he’s stepping into a Church when he has the thought.

The second paragraph is all about Bloom’s strained relationship to the Catholic church. I’m sure that was fairly standard for Jewish people in Europe at the time. He resents the Catholic church for their imperialistic evangelism and for the way some of the priests act incompetent so they don’t get sent on challenging assignments.