No, milk thistle (Sylibum marianum), when used as a spice or dietary supplement, will not affect the effectiveness of Yasmin birth control pills when used in moderate amounts.

Milk thistle contains silymarin, which may affect liver enzymes responsible for drug metabolism, but there is no evidence that when used in supplementation doses or as a spice, it significantly affects the metabolism of hormones contained in contraceptive pills.

I have attached helpful materials:

https://www.gdziepolek.pl/substancje/ostropest-plamisty

https://www.gdziepolek.pl/artykuly/czy-jedzenie-i-picie-obnizaja-skutecznosc-antykoncepcji