The proposal does not mention 501C3's, only 501C4's, 501c5's, and 501c6's.
I believe that most political lobbying groups, such as the NRA are 501c3's. This proposal seems more aimed at unions and such organizations as Planned Parenthood.
So they are covered, as are most of the other advocacy groups in the US.
In addition, the action of any part of the government to forbid any person (or group of persons) from communicating their political views is unconscionable. It is an act of absolute tyranny that is totally in violation of the 1st Amendment. No matter who is affected, it is wrong and cannot be tolerated.