Moreover, it was completely pointless to be shy about this, because if you were conscripted, the norm was to have common showers, so anyone could have a good look at you for much more than the few seconds of the physical exam.
EDIT. I'm serious. Few girls are summoned (e.g. medical related education). They don't have to show their genitals.
I am in no position to judge the procedure on a medical basis but know that it is (or was) near universal for potential recruits and has become a bit of a meme.
Your strong reaction to this procedure is something for you to dwell on.
What the commission might get serious with is enforcing the mustering process, regardless if it is about the medical exam or the aptitude tests.
But anyway:
"The Clash - The Call Up (Official Video)"
Nobody should accept gender discrimination or being touched without consent.
I see a subtle difference between being barefoot and showing cock and balls to half dozen strangers. I know of at least one American president who avoided being drafted because of his "feet situation".
Even touch without consent is explicitly a thing that will be accepted by any sane human. example: someone grabbing your shoulders last second to pull you back from a street crossing before a car hits you that you didn't see coming by yourself. There are even laws in some countries when you do NOT help in acute situations you can go to jail. And at the end it IS touch, without consent.
I just don't get why genitals are such a big deal to begin with. but also baltic sea here, people go naked to beaches or in saunas without blinking since ever.
The doctor would also grab your testicles and ask to cough, to diagnose varicocele. I wonder how many young men have undiagnosed issues since the military exam was abolished.