First, if you look up progressive academic theorists [1] you will see that they are largely inspired by Marxist philosophy either directly or indirectly. The right are diametrically opposed to Marxism because it relies on an assumption that Man can rise above his Animal instincts. But, man can't, even with best intentions (i.e. ethics professors do not behave more ethically than non-ethicists) [2][3].
There is a belief by the right that the great majority of people working in government and government related industries (e.g. NGOs) have come out of liberal arts programs that were inspired by the academics listed. They also believe that progressive ideology has steeped into the sciences.
I believe the right's goal is total dismantling of the executive branch. The point is really to destroy any power that the executive has down to the bare minimum so that the risk of a king is eliminated. It's interesting that they put a group of potential tyrants in charge of all of this - it's almost as if they want to show everyone how bad of an idea it is for the president to have so much control.
They generally believe that differing cultures are a good thing but because of Human nature integration cannot work. Therefore, in a state system, they believe one should be allowed to move to the state of their choice and enjoy whatever culture they want given the constraints of the constitution.
Furthermore, they believe the constitution is the only way for lasting peace. It sets the bare minimum for a social contract that works across cultures and people. It gives a framework where people can be culturally different but equal. And, they hope to expand the US to other countries voluntarily (we hope) so that those countries may also share in its glory.
[1] Achille Mbembe, Angela Davis, bell hooks, Cheryl Harris, Cornel West, David Graeber, Derrick Bell, Edward Said, Eve Kosofsky Sedgwick, Gayatri Spivak, Gayle Rubin, Herbert Marcuse, Homi Bhabha, Jacques Derrida, Judith Butler, Kimberlé Crenshaw, Mari Matsuda, Mariame Kaba, Michel Foucault, Nancy Fraser, Naomi Klein, Ngũgĩ wa Thiong'o, Patricia Hill Collins, Peggy McIntosh, Richard Delgado, Robin DiAngelo, Robin D.G. Kelley, Ruth Wilson Gilmore, Simone de Beauvoir, Thomas Piketty, Frantz Fanon, Pierre Clastres, Antonio Gramsci, Jacques Derrida, Roland Barthes, Claude Lévi-Strauss, Marcel Mauss, Sherry Ortner, Ferdinand de Saussure, Louis Althusser, Gilles Deleuze, David Harvey, Murray Bookchin, Cedric Robinson, C.L.R. James, Paulo Freire
[2] Schwitzgebel & Rust (2014), etc.
[3] This is also why many Christians align with conservative thinking because in Christianity Jesus is the only Good thing of this world, and every person is equally sinful.