It's probably a bad section of thread on either the axle or one of the nuts.

Remove the wheel, and remove both nuts completely and clean them and the axle to be sure no bit of grit is binding the thread. Then spin on the nuts which should spin freely all the way down to the end. If one side doesn't switch the nuts to the opposite side to see if it's a nut or the axle.

A slightly damaged thread often cures itself if the nuts are run back and forth a few times. Oil the thread first to prevent galling and run the nut past the sticky area if it'll do so with reasonable force. If it resists, work back and forth up to the sticky spot going a bit farther each time until past, then back and forth over the entire length.

Once both nuts spin freely, you should be able to mount the wheel without any grief. Don't forget to oil the threads.

Note, your washers inside the dropout contribute to the problem because the only thing keeping the axle from spinning with the nut is friction against the frame. If thread friction is higher than frame friction the axle will spin, and the washers are reducing engagement with the inside of the dropout. Consider moving the washers inside of the axle lock nuts if possible, or at least bind them against the locknut with a drop of cement or a tiny wad of chewing gum. This will also make mounting the wheel easier because the washers won't float outward when the wheel is off.