I'm wondering, how come studying mice breeding was considered lewd when humans had already been breeding a variety of livestock (and selecting traits at this) for thousands of years?

Imagine being the person in charge. You all are bound to celibacy, so you've seen and heard hushed tales of all kinds of ...interesting side effects from living in that state for years.

This guy walks in and makes his sales pitch. He wants to keep mice in the monestary. And have them get it on. Mostly under his personal observation. For science. Totally not some odd perversion, promise.

I would have my doubts too!

He also kept bees in the monastery garden and tried to do experiments on them but it wasn't known back then that bees mate high in the air, so his attempts to breed them were futile. Other monks were often stung or annoyed by the nasty bees so he quit beekeeping.

Source: Mathematics of Life by Ian Stewart. I also visited his museum on Mendel Square, Brno.

Once Upon a Time... The Discoverers ep. 16 also mentioned that the monks were annoyed at eating peas too often but I forgot to ask at the museum if that's true.

Yes but he likely forged some data. Statistics show a high probability of his pea counts with a clear 3:1 phenome split being too good to be true.

Source: Mathematics of Life by Ian Stewart. I also visited his museum on Mendel Square, Brno.

That is amazing! Im sad he never continued.

Well, his research was very sound by modern standards, mostly adhering to the scientific method. It would be very untimely 200 or more years prior. His paper (even in its original form!) is understandable by any modern intelligent person who can read German cursive.