Why would karmamudra ruin the reputation of monks?
No one ever suggested monks engage in karmamudra in the first place.
You have to formally give your monkhood back before sex.
Yes, you must give back your monkhood before sex.
No, you don't have to give back your monkhood before kamramudra practice.
Because karmamudra practice isn't sex
How can that be?
The analogy I was given was of a civilized man trying to reform a thug. As part of the reforming process, he gives the thug a rule; do not stab anyone, defined as "cutting someone with a knife". Good rule, right? Ok, then after some time the thug stops his criminality, goes back to school, gets a degree, goes to med school, graduates and becomes a surgeon. So now he is breaking the rule of not stabbing anyone because he is "cutting them with a knife". No, what he is doing is completely different because of the motivation and skillful means he is employing. He is not "stabbing" them at all! But the next thug you're trying to reform says, "Hey, I can stab people all I want. Look at him!". That's why LTK refused to do the practice, because the next "thug" would interpret it back down to his level of unawareness.
As I am fond of quoting ChNN:A human being has his limits. And thus in every conceivable way, with every possible means, he tries to make the teaching enter into his own limits.
And of all the things in the world that an unaware human being must reinterpret back into his own level of living is what looks
like sex to him.
Karmamudra is not sex. That's why a monk can do it, just like a surgeon isn't breaking the rule of not stabbing someone. Unimaginable, right?