Yes, this is true. Consensus is largely that language can certainly influence thought in language-specific domains, and that it can influence aspects of cognition in other domains, but only to the extent of shifting probabilities and defaults around --- not to the extent of controlling how speakers think or preventing some types of thought according to languages spoken.

Most "grammar nerds" I know are linguists, who think this is neat because they're more interested in how language works on a more fundamental level than individual grammars (though of course those are interesting too). I guess it's possible that conlang types have the opposite view! I was just amused by the distinction between what we think of when thinking "grammar nerd".