Q: Would socialist and communists find a home in the Republican party today?
Funny you should ask.
Remember what party Teddy Roosevelt belonged to? (Ask CM, I think he voted in that election....)
The Progressive/Bull Moose Party started as Republicans.
With the modern GOP, there tend to be certain issues or specific decisions that can spin toward the more liberal ... maybe call them within the communist/socialist penumbra.
In the US, while the overall arc may be toward progressive ideas, we've struck a fairly solid balance between conservative, capital-oriented markets, and socially progressive positions.
(Obamacare was always a bad policy, but it fits into that arc.)