Interesting question. They partially address it in the paper:
> Controlling for gender, ethnicity, and education did not meaningfully alter the relationships between cognitive ability and support for freedom of speech, nor the mediating role of IH. Also controlling for participants’ ideology (separately or in addition to the demographic variables) did not meaningfully alter the results, which can be found at OSF. (p. 39)
I read that to suggest that, at least for study 3's results, the inclusion of education did not meaningfully change their results.
If we are thinking about possible confounders, something I am wondering about the extent to which their choice to use verbal cognitive ability (i.e., "a vocabulary test (i.e., Wordsum)" for study 1 and 2, and "a (verbal) cognitive ability measure, that is, the Ammons Quick Test" for study 3) could explain participants' preference towards freedom of speech, which arguably is usually discussed as a verbal form of freedom, either spoken or printed. As they are measuring verbal capacity, I would expect people who are better with words to be more drawn to freedom of speech. Maybe people who are more "outgoing" might be drawn more towards freedom of assembly.
I am also wondering how people who are drawn more towards non-written forms of communication (e.g., memes, videos, podcasts, etc.) score on their verbal cognitive test and whether they have similar/different views about freedom of speech.