The guidance we get is to call it a day above force 5 on the Beaufort scale (that's "19-24 mph - Small trees sway; crested wavelets on inland water"). I don't normally climb with wind speeds much above that - especially on something brittle, like willow or poplar. I have worked in higher windspeeds, in the past, when I worked for other people. There's often a lot of peer pressure to just get on with it, which is easy to fall for when you are just starting out. On a lot of trees, windy days are difficult, especially if you are anchored on one stem and working/secondary anchored on another. Those stems move like a tuning fork, together then away from each other, so first your lifeline gets slack, then it tries to pull you off the stem.
The worst one was this huge poplar, dbh 4-5', must have been 70' or so..and it was windy- it must have been over 30mph. There was no central stem, but lots of separate, twisting limbs, and I struggled up one of them. Once I'd got anchored in I managed to rig a branch and lowr that, but after being blown off the branch I was standing on, we had to call it a day. The most frightening thing was looking down. The stem I was on was not only swaying, but was twisting around it's axis. It must have been winding up 30 degrees one way, then the other.
With hindsight, and with more experience, I would never have even got the climbing gear out of the truck on that day, not for anyone. But, when you're starting out, you tend to (foolishly) assume that, if you've been told to do it then it must be safe - and no-one wants to look like a coward.