I climb on white pines pretty often and red pines occasionally, and often get some sap on rope, gear and hands. White pines, with fairly thin bark on upper limbs, are especially prone to be sappy. Sap comes off of gear with a bit of rubbing alcohol and elbow grease. Rubbing alcohol with soap and water works for hands.
I've also used rubbing alcohol sparingly on rope, but this will be a bit controversial, so you'll probably want a few more opinions about it. My reasoning is that climbing ropes are generally polyester fibers (at least on the outside), and polyester is said to be pretty insensitive to most organic solvents. You might want to have a close look at what is in the rubbing alcohol - some mixtures have a bit of acetone or other more aggressive solvents in them. Lately, I've just kept climbing on the rope, and the sap wears off before too long. As far as I know, there's no real harm in the stuff as long as you don't have great gobs of it all over (one exception: carabiners - it can make the locking mechanism sticky, which would be seriously bad mojo - but mechanical things are easy to clean up with any number of common organic solvents).
All of that said, pines with A LOT of visible sap on them are probably suffering from a lot of injuries and maybe shouldn't be climbed, both out of consideration of the tree, and out of consideration for the climber's safety and comfort. A healthy pine always has some sap here and there, and that's just part of the experience. Precautions are as for any other tree (stout living limbs for tie-in points). Some pines in some forests will have a lot of dead limbs in the way, and this can make canopy access difficult.
Personally, I wouldn't miss climbing white pines for the world - they're the tallest trees around here (northern Minnesota), and always a rewarding climb.
