Gerrymandering predates the Republican Party, and as the opposite of gerrymandering is also gerrymandering, it was unavoidable. Not to say Republicans haven't done some bad gerrymandering, but acting like it's a Republican thing is just wrong. Who discussed cheating in 2020 is an important specification, because you're not remotely talking about the people making local county decisions about polling places, and your claims of giving themselves the legal power to cheat are just 100% based on insinuation.
No, the opposite of gerrymandering is not gerrymandering. Gerrymandering is the deliberate redrawing of electoral districts with the intent of unfairly skewing an election. If borders are drawn under a principle other than the geographic distribution of party affiliation then it cannot realistically be called gerrymandering. It may for various reasons favour one party over another, but this effect should be incidental: transient or fluctuating over time, with no party consistently disadvantaged, and modest.
You're at least right in that a lot of US political shenanigans are not party-specific. But nevertheless, the cultural attitude of using political power to cheat is ingrained in Republicans even if also the Democrats. Fundamentally, claiming the Democrats also cheat in no way defends the Republicans from accusations of cheating.
And let's be clear here, there already exists comprehensive evidence that your last Republican president attempted to overturn a democratic election by numerous scams and immorally undemocratic devices, up to and including packing an angry mob at the legislature. However, instead of being made a pariah, he is still loved by party members, protected and acclaimed by high ranking party politicians, who are enacting bills in line with his lies. The Republicans are implicitly telling everyone they'd rather cheat than lose. We're doing no more than accepting them by their own actions.