Voting is a much more important right than the other rights, because voting is fundamental to the existence of a republic. One could argue that the right to bear arms exists for the primary purpose of protecting the right to vote.
Voter ID fraud is exactly the kind of thing that infringes on right to vote. Stronger protections on voting is what protects this right, not the other way around.
As someone who not only lives in a country with a widespread voting fraud (done by government officials), but also have been an observer on number of elections and have seen this taking place first-hand, I can't understand how relaxed are Americans about this issue.
> Voter ID fraud is exactly the kind of thing that infringes on right to vote.
There's a difference between "infringing on the right to vote," which is where you're literally preventing from someone from voting, and "diluting a legitimate vote", which is where your vote doesn't weigh what it ought to. Mathematically, it's the difference between scoring a zero and scoring some fraction less than one.
It turns out that, at least in the USA, advocates of voter ID requirements and other unnecessary impediments to voting in fact desire the opposite effect - that their votes be worth more than they would be if widespread voting by qualified citizens were easier than it is.
> I can't understand how relaxed are Americans about this issue
We're relaxed about it because the data (and we have measured and investigated, many times) says that voter fraud here is so rare that it falls well beneath the noise floor of statistical significance.