Some depends on the denomination in Christianity. There is one or possibly two that frown on blood transfusions, for instance. I'm drawing a blank, haven't thought about this in a long long time, I want to say Jehovah's Witnesses and possibly either the Brethren or Amish (this might also include Christian Scientists). By default that pretty well rules out any implantable devices and donor organs.
There are some that resist vaccines, I don't think full denominations, more like subsets. (Other than the Amish, they are pretty much unto themselves, they are very exclusive to the point that their children who turn from the faith are banished)
I'm not aware of any that object to external prostheses, though back to the Amish I think they are resistant to electricity, but I'm not sure how batteries fit the equation (for something like a hearing aid as we typically think).
Just to give some sense, my Great Grandmother, whom I loved to pieces, was resistant to a lot of things we take for granted. She didn't like loud parties, dancing or carrying on with laughter. One might think she was dour, but far from it, she was light hearted and joyous, just not raucous about it. I never heard her swear. Grandpa bought her a microwave to make it easier for her to cook for herself, and she told him "Get that THING out of my house!" She never used it. The idea of tattoos or make-up was unthinkable to her, and her long natural hair was the color G-d intended to the day she died at 92 years old. I'm not particularly sure what denomination she aligned with, but her brother, my Great Uncle, communed with the Brethren.
Grandpa, her son, was Lutheran, as was his wife (my Dad's step-mother), as well as my Dad's half-sister.
My Dad was non-observant, later in life he became mildly Christian, in a generic sense, no particular denomination.
My Mom was a closet Catholic (I was baptized as an infant, funny the Church didn't like my given name so my certificate has my first initial and middle name). She also dabbled in Mormonism. She did take us as kids to a non-denominational Church when I was a pre-teen.
Her Dad I think was Baptist, though he was pretty laid back, not the fire and brimstone variety. His wife, my Mom's step mom, was Christian Scientist.
When I was about 22 I think, I sought out and was baptized, just happened to be in a Pentecostal "Holy Roller" Church. But I've mostly been a solitary, I have too many uncomfortable questions to align with any one specific denomination.
If by genital modifications you mean circumcision, I'm pretty sure that's optional throughout Christianity...nice if so, not a deal breaker if not. I'm not aware of any female genital modification practices, and I've not heard any complaints regarding breast augmentation (apart from medical concerns, back with the leaking appliances). I would generally agree with Thomas that gender modification as a rule is discouraged, but clearly there are some subsets that are more accommodating.
A lot falls onto how the teaching to treat one's body as a Temple is stressed. Where it isn't stressed, the congregation is more likely to be accommodating. Where it is stressed, aesthetic or elective modifications are likely to be frowned on, but by and large medical necessity is still accommodated except in the most rigid traditions. Tattoos, as a rule across the board, are frowned on...but if you got 'em before you became Christian, as long as they are covered most folks look the other way.
So its hard to give a simple answer. This is just Protestant Christianity, I'll leave to Thomas regarding Catholicism.