I know for one that Israeli lobbying groups in the US don't have to register as foreign agents, because they're technically run and funded by American citizens

I know for one that Israeli lobbying groups in the US don't have to register as foreign agents, because they're technically run and funded by American citizens (often with dual Israel citizenship). Taking orders from Israeli officials doesn't change their standing because they have enough plausible deniability. If you can find a Russian counterpart to this with comparable funding or influence here, please show it.