They don't have any political leanings but they do have a philosophical project. If you dig into the site a little you'll find that they're published by the Institute for Advanced Studies in Culture (housed at UVA) and IASC exists to promote research into the contradictions of modernity, by examining how culture manifests itself in metaphor, symbol, ideals, principles, institutions, and material objects [1]. I've been a reader of THR for a few years and I'd say generally they publish articles that promote moral realism and humanism. They're sort of metaphysically open-minded.

[1]: https://iasculture.org/about/vision