You are criticizing someone who is pushing the same anti-“woke” propaganda as you are, except they are using the version from a professional propaganda outlet that has decided that it is more effective when mixed with elite resentment.
I don’t think the term “luxury beliefs” maps one-for-one to wokism or hatred for elites. The key is that the speaker is far removed from the consequences of his actions so is able to espouse edgy but incorrect and even hypocritical theories. For example, in San Francisco blogger Tim Redmond and supervisors Dean Preston and Aaron Peskin are long-time homeowners who espouse anti-capitalist theories in order to justify their actions to prevent housing, which results in higher rents for ordinary workers. I wouldn’t call these out-of-touch people “woke” or especially elite. But I think the term “luxury beliefs” applies well.
See Noah Smith’s examples of luxury beliefs which are not simply wokism: https://twitter.com/Noahpinion/status/1474413184891113478