Some States
For "majority party", please read "party holding a majority in the legislature, and governors office, no matter what they had to do to arrange that, and regardless of the will of the actual majority of voters".
California has a fairly rigorous procedure for redistricting to forestall some of the most blatant abuses, but this is not because the legislature, in its benign majesty, set those rules. It is because California also has the referendum, where a sufficiently large number of voters have signed a petition to get a measure on the ballot, and a sufficiently large number of voters have approved it once on the ballot.
All is not rainbows and unicorns, and some fairly pernicious referenda have passed, and been locked in because they set a larger majority for their repeal than they were approved by in the first place (still a few bugs in the system), but some legit reforms (the purpose for which the referendum was designed) have occurred.
The major issue in the U.S. is that getting a even a slightly bent state government to allow its voters to limit its power is a non-starter. Even more so with SCOTUS disinclined to interfere with that particular form of States Rights. Don't go looking for a corrupt state to allow its voters the referendum if they don't already have it, and don't be surprised if states that do have it make "modifications" to rules to limit those pesky citizens actually accomplishing much.
Even with the best of intentions, the party that allows fair elections in its state has unilaterally surrendered some power to its possibly less scrupulous opponents, and between senate rules, electoral college, and a hands-off SCOTUS, this is unlikely to end well.