A party of the right nationalising a business, considering it, talking openly about it. It was the UK Conservative party who nationalised Rolls Royce, almost immediately sold off cars, and kept Aero Engines a while. Otherwise they'd no longer exist as the RB211 engine had broken them.
Larger government. State ownership does not guarantee incompetent or inefficient. The right used to believe in many of the things that have become unthinkable. The Tories also wanted to improve services, built social housing, added libraries and social care. Pre war UK used to permit the various cities around the UK to form municipal corporations. They were used for power generation, water, rail and tramways among other things, and mostly worked very well indeed -- with the city getting service and income, but being quite hands off from the modern perception of centralised control. See also the various towns and cities that have put in their own broadband, far better than the private sector offer, in more recent years...
Clean Air Act UK was brought in by the Conservatives in 1956. The right used to be much more amenable to environmental and health regulation. Well regulation in general. Now they avoid, neuter and talk down regulation, and slim down the bodies who once oversaw said regulation.
Specific, I think, to the UK, the astonishing degree of centralisation brought in since 1974. Nearly all of it under the Tories. Yet Labour is perceived as the party of state control. Neither party talks of giving real power back to the regions and cities, they both mostly talk against it.
There's other examples on the left, and probably similar examples the other side of the Atlantic.
Not OP, but as a thought experiment, I tried to think of some things that are un-discussable because of one side or the other.
Maybe universal healthcare, completely gov't paid? That's socialism to the right -- can't try that.
On the other side, maybe ending hate crime legislation? Or striking down Roe v. Wade, and letting each state be their own experimental ground? Ending minimum wage?
I am curious, what are some examples?