Not only she doesn't fully approve, she also thinks him "strange" (and almost says it aloud too!). I'd also expect Catherine to feel much more keenly the respect due to Mrs Allen, as that lady as always been kind to her.

Without going into spoilers, I feel Catherine is more likely to become more easy with Mr Tilney, as she is shown not trust her own judgement and to rely heavily on others'. Since Mr Allen approves of Mr Tilney, I'm sure she would have no trouble in putting her own doubts to rest. She has done it at least once, with John Thorpe, who she did not like, but was recommended by both James and Isabella. This had a much greater effect on her opinion than her own feelings.