I have both wood and chain link fences. I can see where the weight of vines that grow larger woody stems like wisteria or trumpet vine might create load issues on a fence. But several mentioned wouldn't seem to pose the same threat.
Always looking for interesting plants for pollinators and food! Bonus points for highly, and pleasantly scented plants.
"Si hortum in bibliotheca habes, nihil deerit." [“If you have a garden and a library, you have everything you need.”] -- Marcus Tullius Cicero in Ad Familiares IX, 4, to Varro. 46 BCE