Are people here sure that this Church is connected with the alleged apparitions? My internet search revealed no mention of the two being connected. Why not go and check it out. Even a phone call could give you a lead. You can always walk away if it's not above board.
I applaud your charity. Till this very moment, I had never heard or read anything even hinting at a characterization of adherence to the Bayside looniness. What is more, to my knowledge the validity or liceity of Father Milagrosa's ordination has never been the object of reasonable
doubt. Note, please, that I am not accusing the admirable Frances of calumny or detraction, but if she or anyone else has something more substantial than what I've read thus far to offer, I think that it should be laid before us all.
I too, for my sins, am a resident of the Big Bagel, and I have met people who hear Mass there, though I am not of their number. I think particularly of two elderly people (i.e., even older than I am and hence close to eighty) who have, as I understand, gone there on and off for years. At other times they frequent an out-of-town indult parish. Since they do the latter, I can't imagine them doing the former without a qualm, especially since they are folks who are inclined to a certain amount of after-Mass socialization. (I'm not so inclined, as I've mentioned on occasion. I go to Mass, and afterwards I go home. Punkt.)
What with the present state of the world, Matto, you must make up your own mind about these questions. You seem a reasonable man, and so I am sure you will make a reasonable decision. But nowadays especially, when finding a properly ordained priest who celebrates an unadulterated Mass is by no means as easy as pie, I find the idea of canvassing (often even grilling) priests and congregations about their opinions on things that may legitimately be considered private—even if they constitute actual or arguably sinful matter—genuinely pointless, besides being distasteful in the extreme. I'd even call it un-Catholic.