A study was conducted examining exactly this question. It turns out the bias is even worse: Not only are the 'wrong' questions unlikely to be asked, studies get rejected if they get the wrong results:
The authors also submitted different test studies to different peer-review boards. The methodology was identical, and the variable was that the purported findings either went for, or against, the liberal worldview (for example, one found evidence of discrimination against minority groups, and another found evidence of "reverse discrimination" against straight white males). Despite equal methodological strengths, the studies that went against the liberal worldview were criticized and rejected, and those that went with it were not. - https://theweek.com/articles/441474/how-academias-liberal-bi...