The working class have property and stocks too and don't want them taxed stupidly.
Yes, but far less. We can have tax free thresholds, you know. Like the capital gains exemption for sale if a house.
Any working class person against higher and broader capital gains taxes is not thinking very deeply, in my opinion.
That's the entire reason why income tax is progressive, and there's no reason that couldn't be applied to any other implemented tax including capital gains.