I don't think one side particularly pushes for voter suppression as an actual goal but if you think they are being manipulated to or they do it out of some misled form of racial, social, or cultural discrimination, well, that could be possible, but I respectfully believe that more American citizens today want equality for all more than yesterday.
The last bit is true, but that's because the GOP and american conservatism in general is physically outnumbered in the US; voter suppression and depression is literally what's keeping them as politically relevant as they are. GOP politicians and pundits, and their predecessors,
absolutely are pushing for voter suppression as an actual goal, and have been since basically the founding of the bloody country, largely because they realize their odious horseshit of an ideology is unpopular and cannot be realized if everyone has a say. That was true at the time of the 3/5ths, it was true during Jim Crow, it's true now when you have open calls among US conservatives for fascism and the deconstruction of american democracy alongside constant attempts to disenfranchise citizens and make the voting process more difficult.
There is not even the shade of both sides when it comes to voter suppression and a healthy electoral system in the US. The GOP and those before it have been attempting to sabotage our democracy for political gain for decades to centuries, and they're only getting more desperate about it as public sentiment builds further against them and the numbers to
enforce that continues to grow.