Thank you for your well-thought-out post. When I think of Mary, I do look at it a little bit from Edmund's sympathetic POV where he believes to begin with that Mary has just had bad examples that have jaded her view. A prime example that Mary has for clergy is Mr. Grant, who she has been personally critical of. I think her general criticism of clergy stems directly from his example, particularly her description in Ch. 11. I felt that this perhaps perfectly expresses her opinion of Mr. Grant:

“Oh! no doubt he is very sincere in preferring an income ready made, to the trouble of working for one; and has the best intentions of doing nothing all the rest of his days but eat, drink, and grow fat. It is indolence, Mr. Bertram, indeed. Indolence and love of ease; a want of all laudable ambition, of taste for good company, or of inclination to take the trouble of being agreeable, which make men clergymen. A clergyman has nothing to do but be slovenly and selfish—read the newspaper, watch the weather, and quarrel with his wife. His curate does all the work, and the business of his own life is to dine.”

I also have felt that it is telling that Mary really is rather thoughtless about a greater sense of things, and backs up your assessment of her contempt or indifference to religion as well.
In Ch. 22 "I see no wonder in this shrubbery equal to seeing myself in it." after Fanny waxes almost poetic about it.