I know this is a little different, but my mom is a family doc, and she's friendly with (nearly all of) her patients, in that she'll happily say hi and talk to them if she runs into them in town, etc. (I joke that I can't take her anywhere - we've even been in different states and we've met someone she knows!

) She won't initiate relationships with patients, because that would violate ethics rules, but there have been patients who have invited her out and she's gladly accepted, and has become friends with them. And, of course, lots of people go the other way - they're friends of hers (or mine

) first, and then become her patients.
Midwifery, of course, is
even more about intimacy and having a good relationship between client and care provider (though rare, my mom has patients who just chose her because she takes their insurance, or is close by, or something like that), so I can hardly imagine a midwife, especially a homebirth midwife, who would think it weird one of her clients would like to get together for lunch or dinner or coffee or birthdays or something. I suppose there may be some who wish to have more of a work-personal life seperation, but that doesn't seem to be the rule among women who are drawn to this profession.