For example, it was only a few years ago in the US that being openly gay stopped being someone which would get you kicked out of the military. Couldn't anyone during Vietnam just have said they were gay?
HA! Plenty of people tried that, all the time, all the way up until DADT was repealed. If you were scheduled to deploy, it just got you demoted, loss of pay, extra duty, still deployed, and then you got kicked out after you got back. The rule was never been consistently enforced (which was part of the problem with it), because commanders are the ones who had to initiate the process. This is something most people don't really get about the military: barring felony level misconduct, any action of the sort is entirely on the commander. So, if a soldier was a good soldier, command might well have given zero fucks and kept him in. If the commander thought he was trying to get out, he'd probably give zero fucks and keep him in. If the commander was feeling lazy and didn't want to do all that paperwork, he'd give zero fucks and keep the soldier in. In short, your commander decides if you go to war or not, and guess how he's going to decide 99% of the time? In peacetime, yeah, he'd be more likely to take action (unless he has more important things to do, like pretty much anything else
Rules may be rules, but command isn't so stupid as to not see when someone is trying to avoid going to war, because it's usually pretty blatant. Since it's up to them to act upon the misconduct, they're not exactly likely to do kick someone out.
They also had a ban on facial tatoos, for instance,
How many people have you seen with facial tattoos in jobs that are at all considered upstanding? Yeah, it might keep you out of the draft, but it will also keep you out of employment. It's not exactly the type of strategy most people are willing to pursue.
various medical requirements which were surely easy to intentionally fail.
Doctors aren't idiots, and doctors in the employ of the military generally aren't going to overlook this kind of thing.
With so many rules, how could someone not avoid getting drafted if they so desired?
Because while the military loves rules, and loves making rules, and loves enforcing rules, they almost always prioritize their mission first, and if they need warm bodies, then they're going to ignore things like "claims to be gay" or "claims to have X medical condition". No matter what idiotic policies they may come up with to do their job, no matter how dumb commanders may seem at the time, they're not that dumb.