Are there any downsides to ignoring your friends in GTA 4?
You miss out on the perks, like the weapon delivery you mention. Also there are Achievements & or Trophies depending on what platform you're playing on.
After that, I do not believe so. I think (but need to verify) that as you ignore them how much they like you will drop, and if it drops too low they won't be your friend anymore if you change your mind and want their friendship after all.
Still, my thought would be, on a second playthrough, don't worry about the ones you don't care about.