Let's be very clear about what Buckley was trying to accomplish.
Some context.
Conservatism had been in the wilderness since the progressives took over with Teddy Roosevelt. It wasn't until the Goldwater campaign that Conservatism had gained any traction.
How did Conservatism gain traction? Specifically, how did they break the New Deal Coalition and flipped the Solid South. It was accomplished partly by using the Southern Strategy (aka exploiting Civil Rights backlash).
But it was also Religion.
To be clear: the Right replaced the old anti-corporate populism with religion, that is, religion became the new populism for middle America, thus prefiguring the partnership between Reagan and Robertson.
And Buckley was the megaphone for this new religious populism.
(It should be noted that the Left - by moving away from religion in the sixties - opened the door for Buckley/Goldwater and the Conservative movement.)
Ayn Rand was a Libertarian, and an atheist (which put her in direct contradiction to the religious populism Buckley was using to get middle America into the voting booth). So of course Buckley and Rand could not form a partnership.
In summary: Buckley used two things to build Red State America:
1. Anti-communism (which morphed seamlessly into anti-terrorism)
2. Religion (which is a bedfellow of "Tradition")
(It should also be noted that Reagan was not nearly as willing to cast Rand, the Libertarian Queen, overboard. Reagan needed Buckley's conservatism as much as he needed Rand's Libertarianism. In fact, he used Conservatism to get the poor into the voting booth. However, once the election was won, Reagan used Libertarianism to create the low tax, anti-regulation infrastructure required by business.)
It was a brilliant partnership built out of God and Money. Jesus is turning over on his cross.
People might ask: but how did Reagan get away with this contradiction? Surely the voting public would see the blatant contradiction between Religion and Libertarianism. Turns out, the Reagan Revolution had an answer for this problem too. They built the most powerful ideological bubble ever created, and they filled it with wildly charismatic pundits who forbid Republican Voters from going to any outside media source. They did this by conditioning the GOP voter to fear non-Conservative media sources as evil. This gave them the ability to put their voters in a hermetically sealed bubble where the contradictions between Conservatism and Libertarianism were never exposed.
It was ******* genius. Say what you want about the Right, but do not underestimate how brilliant their strategy was. They just needed enough naive, under-educated voters to buy into it. It worked better than anyone could ever imagine. In fact, GOP voters still don't see the contradiction. They literally only think in the terms which they are given by Limbaugh, Hannity, Coulter, Beck, Savage, etc. This is what populism is meant to do: appeal to voters emotionally so they can be locked in.
Rand's problem was that she was an honest Libertarian. She refused to play ball with Conservatism and its dream of state sponsored Christianity.