BABIP doesn’t factor into FIP at all, as it’s just a function of Ks, BBS and HRs, none of which are part of BABIP. The theory is these are the only 3 outcomes a pitcher can control, or that at the very least, are not influenced by defense.
That a pitcher can control home runs feels debatable to me. I mean, wind can be a bigger factor in home runs than the pitcher…