It's fundamentally unknowable how much science is being denied the imprimatur of good science for ideological reasons while "actually" being good science. The best you can hope for is examples that meet a lower, more reasonable bar that point to problems in the culture of academia, from which you can extrapolate chilling effects.
There are examples of things like this, as in Case & Deaton's description[1] of the reaction to their study on declining mortality amongst US whites:
> Deaton: Anne presented the first paper once and was told, in no uncertain terms: How dare you work on whites. Case: I was really beaten up. Deaton: And these were really senior people. Case: Very senior people.
This example is just off the top of my head, and it's a blatant example of a study that _isn't even saying anything that taboo_, except among those whose brains have been thoroughly liquefied by politics. If examples as dramatic as this exist, at well-known, highly-regarded institutions, for a paper _published by a Nobel Laureate_, it's not unreasonable to conclude that there's some degree of unobservable cases that were actually successfully blocked, along with chilling effects changing the direction of research in the first place.
[1] https://www.washingtonpost.com/news/wonk/wp/2017/04/06/how-d...