Is it safe to mix vegetable and animal fats? There are so many russian internet-resourses that - without any proof - warn about mixing the above, because it can "drastically increase the fat absorption", but I couldn't find the same claim in english internet.

So now I am confused, if it is safe or not and, more important, why.
Safety, from the perspective of this site, is short term.  Will you get acutely ill if you eat something, within about 2 days?

From this perspective, there is absolutely no safety issue with mixing fats of vegetable and animal origin.  Frying a steak in vegetable oil, or sauteeing vegetables in bacon fat is perfectly safe.