The water in a shower is hot enough to cook it, so it can block the pipes.

100% untrue.

While you're right that proteins can caugulate a little, this is a common urban legend that was started with a prank note left in a dorm bathroom many years ago.

https://www.reuters.com/article/fact-check/housing-violation-notice-in-college-bathroom-prank-resurfaces-idUSL1N2MY2GV/

https://deadspin.com/will-semen-destroy-your-shower-drain-1795434004/

"Abraham Morgentaler, an associate professor of urology at Harvard Medical School and the director of Men’s Health Boston, debunked the rumor for us once and for all. In an email to Slate, Morgentaler says that not only is semen never thick enough to clog a drain, but that 20 to 30 minutes after ejaculation, it will become a runny liquid and slide away:"

I can't understand how we got to the point with this that people have written thousands of articles about it and consulted with medical professionals. We really need better education in this country.