Yes, high blood pressure would keep you out of the draft back then. I’m told the reason why is that if you served 90 days, and then they discovered you had high blood pressure, they might have to medically retire you.
There were a slew of things that could keep you out. From acne on your back (severe I suppose, so as to not be able to wear a back back) to problems with your feet that prevented marching. There were some mental issues and some related to IQ. Back at that time, attorneys made a practice out of helping those who did not want to go into the military avoid service. There were special doctors sympathetic to the anti-draft movement who likewise provided medical opinions/diagnoses (but not treatments) seeking to help a person be excluded from the draft.
Early on, just being married would exclude you, but that quickly changed to married with kids. That quickly evaporated and marital, parenthood status didn’t matter at all.
IQ was another factor they tested for. However, they got around that with McNamara’s 100 thousand. (google it, it’s pathetic)
The problem was that anyone graduating from high school basically has his life in turmoil for a few years. Either he went to college (2S deferment) or he enlisted, or waited to be called. Finally they set up a lottery which resulted in a drawing of birth dates, and, in that order, being called to serve.
I remember smoking some @#$%@% on the government bus on the way to the Induction center in LA for the physical. (that’s where the mandatory pre-draft physicals were given) That was a real joke. Can you write your name and pee warm pee? Cool your government needs you. You walked into the entry way and there you were stopped by a Sergeant. He pointed to two doors. one (the right) led to the medical processing area. The one on the left, led to a glass room with benches and about a half dozen souls sitting there looking like they were waiting for a bus to hell. The sergeant pointed out that we could behave and go home that night, or, if we didn’t, we would be told to sit in the glass room, and later that night we’d be picked up and transported to basic training. We all behaved rather well.
It was a shitty time for young men in America.
ETA, broken bones, things like that would just get you rescheduled a few months down the road. Depression, I doubt it. Asthma, possibly.