I do not get that idea to punish anti-war protesters by drafting them into military by force and send them to the war.

The last person you want to send to fight in a war is an anti-war protester. Though knowing russian war commander mentality (i.e. kill disobedient soldiers) - it could be a literal death sentence [0][1].

[0] https://www.reddit.com/r/ukraine/comments/t9de02/hero_ukrain...

[1] https://www.reddit.com/r/ukraine/comments/tacjiy/this_ru_off...