Calvin Coolidge wouldn't even support today's conservatives. He was against free trade and believed the rich should bear all of the tax burden.
And we all know Barry Goldwater hated the GOP by the time he was put in the grave, much less what he'd think now.
Protectionism was the pro-business, neoliberal position on trade in Coolidge's age, so let's not act like this was some position comparable to modern Democrats.
I would hardly call it the "neoliberal" position, but yeah it was definitely favored by business types. It is important to remember that the Democrats were those who largely held the "liberal" line on trade, which would've been opposition to competition stifling tariffs that forced the American workingman to pay more. Hell, the "populists" were actually some of the more pro-free trade elements of the Democratic Party, arguing that protectionism led the way to monopolies and other consequences of crony capitalism.
And as for the whole part about how the rich should pay most of the taxation, it's worth noting that in Coolidge's day the richest of the rich only paid about 25% income tax, though the poor barely paid 1% of their income.
No, I'm not making that up.