I don't think voters register by party in most states. They certainly don't in Illinois.
If you went by number of GOP ballots cast in primary elections vs. number of RAT ballots cast in primary elections, the RATs have a big edge though. I think even traditionally "solidly Republican" countries have a clear majority of RAT primary voters.
Wiki has a table
Looks like 27 states register votes by party. As it’s been said a lot of older former rats never switched their registration.
And as far as I know, rats don’t usually cast more primary votes in Republican areas