You gave me a giggle with this one, but your question is a good one.* I did a google search with the term:
pole beans + cling
and found these sites.* I clicked on the 'cached' selection and found that passiflora climbs by stem tendrils and pole beans climb by twining stems.
So your trees should be fine.* :)
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.