Peter, unless it gets super hot I don't see how it could damage an annual vine. The only issue I've had with treated/painted trellises are when they were painted black and got super heated and burned the growth. Chaz

I was about to ask this as well. I am painting mine with dark walnut.

I would suggest that you only use stain. Polyurethane will be peeling and ugly within 2 years.

Thanks for the heads up!

I was talking about the rub-on polyurethane, which is not exactly intended for outdoor use but indeed still seals the wood, especially the cut ends of the wood where it's most vulnerable. The rub-on stuff penetrates, and the wood doesn't get much of a sheen. What I was wondering is if the vine twines would the residue from the polyurethane (petroleum distillates, etc.) have some adverse effect on soft stems, but giving it a second thought I think as long as the finish has had plenty of time to cure it wouldn't be much different than having a trellis with a plastic coating.

I've used it. The rub on kind will start pealing and be ugly within 2 tears. I've tried, brush on, spray on, and rub on, and they all peal. If you really want polyurethane, that might last, they make some for finishing wooden canoes, but it is very expensive.
Jim