Right wing in this case meaning the actual terminology (capitalist), not the American terminology of right vs left-wing being a question of social issues
Right wing vs left wing has always been relative to the status quo. Capitalism was left wing when feudalism was the norm. And now Regulated Capitalism is left wing compared the norm of Unregulated Capitalism.
The people who are bothered by OP are making imperfect the enemy of good. What they're proposing is still progress.
And you wont get enough allies to get anything done. This is what Divide and Conquer looks like. It's only a half measure if you stop at the first accomplish. Let the populist get a taste of a social safety net again and they'll want to push for more the next time.