Why don't the heads of phospholipid bilayers repel hydrophobic molecules?
Your question is rooted in a misundertsanding of the hydrophobic effect. Hydrophillic and hydrophobic molecules do not repel but, rather, attract one another through van der Waals interactions. The tendency of hydrophobic molecules to aggregate in aqueous solution (ie the hydrophobic effect) is, instead of some repulsive force, actually driven entropically. I don’t think I will go into this in detail since it has been explained well in many places. That said, it is also explained very poorly in many places (which I suspect you have encountered). I recommend this website to learn about it and other intermolecular interactions.

Once you have a firm grasp on that, consider that in order for a hydrophobic molecule to reach a plasma membrane, it must already be solvated by water. The transfer of a hydrophobe from one hydrophillic environment (water) to another (head groups of the phospholipids in the plasma membrane) should be energetically negligible. The limiting step for passive diffusion across a membrane is transfer from the hydrophillic environment of the phospholipid head groups to the hydrophobic environment of their tails. In fact, the rate of diffusion across a plasma membrane increases with hydrophobicity.