Hey Ben,
Thanks for posting! It sounds like you're unable to change playlists when the car is moving, since it's greyed or dimmed out. We'll do our best to help out with this.
First of all, your safety and your passengers' safety is top priority. Always ensure that you test the following with a passenger to handle it instead of the driver. It could be fun to take a drive and test things out!
Does this only happen when you have Do Not Disturb While Driving enabled? The passenger can turn off this feature while you drive to test it out: How to use Do Not Disturb While Driving You could always create a shortcut for this feature in Control Center to make it easier to test. Check under section, "Turn it on and off in Control Center".
If you're using CarPlay, since it's supported with your 2020 RAV4, then try out: If you need help with CarPlay
Lastly, make sure the content you attempt to play is already downloaded. Not streaming, since this could be related to those cellular settings. (If this only happens when streaming the playlists, then you can enable cellular in Settings > Cellular > Music and/or Settings > Music > Cellular Data.)
Let us know if this helps out!
Wishing you the best and be safe out there, take care!