I contacted moviesanywhere and they emailed me back this response. I'm not for sure but I'm guessing maybe Apple TV Plus is having the same issue. I haven't had much luck getting a hold of their customer service. The issue appears to be Roku's fault.
"Hello Josh,
Thank you for providing the device information.
We have checked this with our team, and we can confirm that after a recent update, some Roku devices no longer support UHD (4K) playback due to a lack of up-to-date Digital Rights Management or DRM specs. We can confirm that your device is included in the list."
As our movies are DRM protected, you will get the error "This device does not support 4K playback" on the 4K movies. Since the data on our service is proprietary and copyrighted, your device needs to be secure enough to play it. The DRM specs on a device are added via updates through the device manufacturer, and when and up to what version of that a device gets updated is up to them.
You can continue to use the Movies Anywhere app; however, you won't be able to play your 4K movies in such resolution, but you should be able to play them in HD. We also encourage you to use your Digital Retailer library, as you may be able to play the movies in UHD using the retailer library.
Please let us know if you have any other questions."