I also had my DisplayLink stop working with the last 10.13.4 Beta, which was a bit of an annoyance, but I was pleased to find that I wasn't the only one.
I'm happy to report that with the latest 10.13.4 Beta (17E150g) update the problem seems to be resolved. It came out in the last 12 hours.
I'm using a USB-DVI on an older Mac mini, and I'm very pleased to have back the use of the second monitor.