I couldn't find a post for VS Community, so I'll post my solution here.
First, you need to go to Tools -> Options -> Environment -> Keyboard, then find the command
Window.NextTab
. Near the bottom it should say "Use new shortcut in: ". Set that to Global (should be default), then select the textbox to the right and hit Ctrl + Tab. Remove all current shortcuts for the selected command, and hit Assign. For Ctrl + Shift + Tab, the command should be Window.PreviousTab
.
Hope this helps :) If there's a separate post for VS Community, I'd gladly move this post over.