The evidence given at their trial was very tenuous. It was based essentially on the testimony of two very shady characters (David Greenglass and Harry Gold). The former admitted later to perjuring himself on many points; the latter was just a not very reliable witness (Gold was a damaged sycophant who would tell whomever he was working for whatever they wanted to hear — a very interesting character, but a witness it is easy to be skeptical about). Even with the decryption information that was released in the 1990s (and was not at all part of their trial evidence), it is not clear that Ethel Rosenberg was involved in any serious way — all of the evidence used against her was provided by Greenglass, and he later admitted he fabricated it and increased her role because if he did so, his own wife would get off the hook.

Even if one assumed they were spies of some serious sort (easier to do since the 1990s than in the 1950s), they were spying for a nation that was an ally at the time. Klaus Fuchs, for example, was convicted of far more serious espionage in the UK and was sentenced to 14 years in prison (and he only served a few of them before he was released). The prosecution was done during the height of McCarthyism, so if you were someone who opposed McCarthyism (as were many Americans) then you saw this as being an extension of that injustice and extremism.

Separately, killing a spy means you can't later interrogate them. You are cutting off a potential source of future intelligence. There is a strong argument, a priori, for not executing spies for this reason — instead, you make their life miserable and then try to get them to cooperate down the line. The fact that they would have two orphaned children on the outside could have been used as leverage once the publicity faded. Who knows. It's a missed opportunity to learn more about Soviet espionage networks.

Lastly, it should be noted that the Rosenbergs are literally the only people the US has executed for conspiracy to commit espionage. It is a very anomalous ruling. It is essentially unheard of in the modern era to have capital punishment for a non-violent crime in the United States.

For what it is worth: We know now that Julius was definitely a spy. I still think it was dumb to execute him (I think it is dumber that he didn't cooperate, but that's a separate thing). I think Ethel might have known a bit about what was going on (and thus not totally innocent), but wasn't really that involved. I think it was excessive, unnecessary, and cruel to execute her.