Sorry to burst your bubble, but back in the 90's when those restrictive laws were put into effect, the Democrats controlled the Oklahoma Legislature but to be fair I'm sure they couldn't have done it without Republican help. Your immediate blame of Republicans is a large part of the problem. So many people refuse to vote for a third party because they are scared the "other" party will take over and ruin everything so they vote for "their" party no matter what.
Not bursting my bubble. Just because one party put in place, that doesn't mean the other doesn't hold onto it for their own benefit now that they control basically everything in Oklahoma.
For what its it's worth, Oklahoma has sent only one democratic senator to Washington since 1973 and that's Boren. It's voted only republican for president since Nixon. The state was clearly flipping even more Republican in the 90s and the party now has a stranglehold on the state, much like Democrats do in California or New York.
The effect of those rules now is that your only chance at influencing who wins an election is in republican primaries, elections for which turnout is low and made lower by restricting primary voting to only registered Republicans. By limiting third party and independent candidates, it then limits the options of who has a legitimate shot at the subsequent general election to basically only the Republican nominee. Living in other states, I really was surprised at how much easier it is to vote in another party's primary or to have a third party on the ballot.