I have some friends who are able to use Pokémon who are 2000 CP+, but I have only been able to use my “Great League” battle combos.
There's a bug when battling Team Go Rocket in Pokemon Go. If you have preset Great League or Ultra League teams, it'll prevent you from using stronger pokemon than would qualify for those leagues. You can fix the bug and use all your pokemon by clearing out your premade Great/Ultra League teams.
Edit: This bug has been fixed since this answer was written, so it should not be a problem anymore.