We would recommend checking for a system update on your Roku device (Settings > System > System update > Check now).
I've been having this problem for weeks now, and had given up on system update. When clicking on "Check now," it would tell me my system was up to date. And YouTube would still not work.
For reasons unknown, I thought I'd try, before going through the Remove/Reinstall rigamarole, the system update again.
And this time it worked. I saw the progress bar go from zero to one hundred percent, and when it was done, YouTube opened normally. Well done, Roku engineers.
Now to see how long it will stay fixed. My fingers remain crossed.