There seems to be a lot of us who are having issues watching HBO Max on our Roku devices. The following info is from their support site, 'Watch HBO Max in 4K HDR' page:
Watch HBO Max in 4K HDR
You can check out the page for further info, but there is info that may be helpful.
"Supported 4K devices
You can watch in 4K on the following devices:
Amazon Fire TV Stick 4K and Fire TV Cube
Android TVs, including: AT&T Streaming Box
Apple TV 4K
Google Chromecast Ultra and Chromecast with Google TV
Roku Ultra 4800x, Roku 4k TVs, Roku Premiere, and Roku Streaming Stick+
Xfinity X1 (Xi6) and Flex
We’re working to add more devices and 4K movies in the future.
Note Dolby Atmos is not available with Chromecast with Google TV, Roku Premiere, and Roku Streaming Stick+."
and for additional tips (bold added by me):
"Step 4: Try another cable or HDMI port
If you're using a streaming player (e.g. Apple TV):
Make sure you're using a High-Speed 4K HDMI cable.
Make sure your HDMI cable is plugged into a HDCP 2.2 compatible HDMI port on your TV or audio/video receiver. HDCP 2.2 may not be supported by all of the HDMI ports on your TV (refer to your owner's manual to find out which HDMI port is HDCP 2.2 compatible).
Bypass your audio video receiver, HDMI switch, or sound bar, by connecting your streaming device directly to your TV.
If you're getting an HDCP error, try the TV steps in this article: I'm getting an HDCP error."
Not sure if these tips help anyone but I figured it'd be worth a try. Since no one is actually 'supporting' HBO Max on Roku, we'll have to figure out the issues ourselves.