These rails are replacing some damaged ones and I would like repaint the whole fence. I was told not to paint the bottoms of the support boards and rails so the moisture can escape. Is this a good idea or do you suggest something else.

Don't use paint, use solid stain. Allows better breathing and doesn't seal the wood so tightly.

Either what ma0641 says or wait a year. You can not paint treated lumber until its completely dry and seasoned