Well, it's worth noting that Oppenheimer never tried to convince the US government not to develop nuclear weapons (he was opposed to a crash program on the H-bomb, until he wasn't), and Einstein and Russell were not really government scientists. So there are some category issues here...!

But more broadly, was there dissent to the Soviet nuclear weapons program, from without or within? In the early days, no to both — there weren't a lot of outright dissenters at all during the Stalin years, for fairly obvious reasons, but even beyond that, the general Soviet point of view, which was echoed in its scientists who worked on the program, was that whatever qualms you might have with the Soviet state, they definitely didn't want to get nuked by the United States, and the best answer to that was probably to have their own nukes. The formative idea for many Soviets in this period (including Stalin himself) was that they had let their guard down with respect to the Nazis and had almost been destroyed for it, and so getting purely defensive nuclear weapons (as they, and not the US, saw them) seemed like a no-brainer.

In the 1960s, when the Soviets had something more like strategic parity, you did get people on the inside and outside suggesting that the arms race was crazy and should be more limited. The official Soviet position was that they only participated in the arms race because the US did (and the US, in this period, still had many multiples more nuclear weapons than the USSR did), and it only takes a little bit of a push to start suggesting that both programs were equally bad. This is sort of the position that weapons designer and dissident Andrei Sakharov eventually came to; really just an extension of the official "nuke are bad but a necessary evil" line, just lopping off the qualification.

It isn't clear to me how widespread such views were. Certainly by the 1980s, with the massive heights of the arms race, coupled with the gradual increase in tolerance for points of view critical of the USSR, you see more anti-nuclear activism in the Soviet Union. Some of this, again, is actually supported by the Soviet state, because it puts the blame for nuclear weapons on the USA and casts the USSR as being purely defensive. But some of this was more broad in its criticism.

In general, in both the US and Soviet systems, the scientists who worked on these weapons systems tended to be in favor of their necessity. It is the rare scientist who actually worked on them and then went against them, and even then it was in both cases mostly scientists who had agreed they were necessary at the specific time of their creation (either to fight the Nazis and Japanese, in the US case, or to counteract the USA, in the Soviet case) who soured on them later, rather than scientists who came to the nuclear complex after the weapons had already been invented (because that is a somewhat self-selecting subset of people). In the 1960s-70s, there was some extra latitude given to dissent to Sakharov, for awhile anyway, above and beyond what the regular population would have been allowed to have, on account of his many awards and his prestige. But even he was sent into internal exile from 1980-1986. Oppenheimer lost his security clearance, and some other US scientists had their passports revoked during McCarthyism, and some got interrogated and blacklisted by HUAC, but that is the only partially comparable thing.

Overall you can say that the Soviet scientists outside the system were generally not permitted as much latitude as American ones were, but that's the case of all political disagreement. The US had a much broader independent anti-nuclear movement than the Soviet Union did, but that's not that surprising.