Ovinomancer
No flips for you!
It says you can't cast any spells besides std-action cantrips, that seems pretty comprehensive.
The question begged, of course, is whether or not reactions are part of your turn. I do not see them described as such, but rather something you can do when their trigger occurs once per round, that timer resetting at the beginning of your turn. Your turn is described as a move, an action, a possible bonus action, and various ancillary things in conjunction with those. A reaction is a special action that can occur on your turn or on someone else's. There's a strong argument that reactions are not part of your turn even if they occur during it.