To understand Mansfield Park and Henry Crawford, you must accept that for many men in his time period, sex and love could be completely separate in their heads and Jane Austen, while she definitely didn't agree with this, knew it was a real way of thinking and presents it as such.
Henry loving Fanny is confirmed by the narrator and without irony. He loved her, "rationally and passionately". He also slept with another woman. To him, this is entirely compatible:
He was entangled by his own vanity, with as little excuse of love as possible, and without the smallest inconstancy of mind towards her cousin.
This view is confirmed in In The Time Traveller's Guide to Regency Britain by Ian Mortimer, where the author explains that in that time period, visiting a prostitute for "just sex" was seen as morally better than having a mistress, because it interfered with the emotional bond of a marriage.
Mary Crawford knows this and is expecting it to happen to her, just like it did to her aunt. She is cynically hoping that at least whomever she marries is rich and discreet. It is only in Edmund that she learns to hope for better:
for Mary, though perfectly resolved against ever attaching herself to a younger brother again, was long in finding among the dashing representatives, or idle heir-apparents, who were at the command of her beauty, and her £20,000, any one who could satisfy the better taste she had acquired at Mansfield, whose character and manners could authorise a hope of the domestic happiness she had there learned to estimate, or put Edmund Bertram sufficiently out of her head.
This is a conflict between city/country morals, which has been a theme throughout the entire novel, but it doesn't undermine Henry's claim of love, only the quality of his ethics.