Of course the first itself is largely hillariously unenforceable even a century ago because of global speech and the First Ammendment - which is a good thing.
I don't think that carve out would be constitutional unless it was even more broad. Say "personal capacity political advocacy is protected" so you could get fired for saying "<Company> supports Free Tibet" without proper permission/authority but "I, not speaking on behalf of <Company> support Free Tibet". Even that would open itself to damn uncomfortable side effects legally for a weatherman opening every broadcast with "I support the reestablishment of Rhodesia!" being protected as well.
> the first itself is largely hillariously unenforceable even a century ago because of global speech and the First Ammendment
The Logan Act [1] has been on the books since the 19th century, though it remains Constitutionally controversial.
Broadly speaking, however, there is difference between punishing certain views and expanding public-sphere protections around free speech. The latter is done e.g. with union-promotion laws, which restrict companies' abilities to suppress certain kinds of union-organizing speech. That precedent could certainly be extended to this issue.
I don't think that carve out would be constitutional unless it was even more broad. Say "personal capacity political advocacy is protected" so you could get fired for saying "<Company> supports Free Tibet" without proper permission/authority but "I, not speaking on behalf of <Company> support Free Tibet". Even that would open itself to damn uncomfortable side effects legally for a weatherman opening every broadcast with "I support the reestablishment of Rhodesia!" being protected as well.