I was having the same issue. I restarted my Roku and it solved my problem. No more subtitles.
When your show is playing, press the up or down arrow on remote, go up to closed captions in the upper left screen and switch to off.
Tried that it won't bring up a menu for me
Same exact behavior as another reported. Empire Strikes Back closed caption would not turn off with the usual controls. I exited the app and then went back in and it stopped. I had to completely exit Disney+, did not have to restart my Roku.
Hey there i had the same issue today, subtitles came on out of no where, there are NO options in the Disney+ app on my roku to turn them off, or any other settings that can control settings like that, the only thing i could do was press * on my roku remote and that is took me to the settings for the tv not the app, and of course the closed captioning option was turned off, i tried to update the app, it was up to date, i tried unplugging the tv, i reset the roku from the roku home screen, i tried checking my disney+ app settings from my account online again no such options, and i tried every other suggestion i could find from the internet, NOTHING worked, so i removed the Disney+ app from my roku, and then readded it, logged back in and subtitles were gone, apparently this is a glitch within the app itself, u can remove the app by going to the roku home screen, go to the Disney+ app, press * button on remote, go to remove channel or app option, click on it, then go to roku home screen search, type is Disney+ and proceed to download the app.
When all else fails...turn TV off and then back on... we watched 2 movies back to back and then the 3rd, we had the caption issue and everything was up to date.
Mine said it already had the latest update but the subtitles turned off! Thanks!