Does anyone know if opening your gates at the airport prevents wasps like it did in Animal Crossing: New Leaf? I'm trying to obtain wood but don't want to get stung.

I opened my gates Locally, ended up getting wasps anyway. It might work on Online, but I doubt it, unless you actually have visitors.
Only one way to find out!

What I do is go around and catch all the wasps first, before harvesting anything.
Someone on here said that the poppers will make the wasps disperse, I haven't tried that yet though.

I've only been able to escape wasps once, by running into the museum. Probably because you don't have to open the door.

I get stung by thwm about every oter time.  if you're quick with a net you din't det stung,,,or you ca rub fast to the nearest door way

Put your net to the left or right of the axe in your inventory, that way, you can easily switch to it with left or right on the dpad. Make sure to run directly upwards so your character faces downwards when you change tools. just learn the timing from there

I shake the trees with a net already in my hand, and face the tree with your characters back to the switch screen so when they drop there easy to catch by just pressing A. As the wasps turn your character towards them for you.

Run upwards and open your POCKETS to switch tools. I've found this seems to give a much bigger window of time, though I may just be saying this because it's the method I've gotten used to.

"I opened my gates Locally, ended up getting wasps anyway. It might work on Online, but I doubt it, unless you actually have visitors."

I did this and personally didn't get any wasps with just having my gates open to online. But I could have been lucky. Worth a try either way.

"I shake the trees with a net already in my hand, and face the tree with your characters back to the switch screen so when they drop there easy to catch by just pressing A. As the wasps turn your character towards them for you."

This. If you position your character in front and slightly to the left or right, with your net out, when shaking, it's virtually impossible to miss, as you will turn to face the wasps when they fall out.
So best strategy is a quick run around town, shaking every tree, before doing any woodcutting.

you can always buy party poppers and use them to scare off wasps. Dunno why that's a thing but it's funny.