It would be really simple for both parties to stop, at least for Congressional districts. Just pass a bill in Congress mandating independent or at least bipartisan commissions with strict rules against drawing seats to protect incumbents, favor political parties, etc. They could even pass a constitutional amendment to that effect.
But only Republicans seem to be resisting that effort. It's not even a difference of opinion on specifics. It's a flat out refusal to even consider the idea.
House bill HR1, which passed the Democrat controlled House, would've established independent commissions in all states (with mandatory public input), and banned mid decade redistricting unless ordered by a court.
The Democrats are at least "trying" to achieve fair districts, Republicans are the ones perfectly happy to keep rigging the maps.