What is taboo often depends on context and there is some disagreement about what deserves the label, but it’s well-defined enough for an answer.
Please don't go into detail. Just give me a vague idea so that I can do my own research.
I will keep this in mind.
Plato’s Republic contains a famous philosophical discussion in favor of some censorship. Ironically, Socrates, who Plato deeply admired, was put on trial and executed for corrupting the minds of Athenian youth and defying the state in attempting to censor his philosophical teachings. The Greek playwright Euripides famously argued against censorship in antiquity. John Stuart Mill is famous for arguing against censorship. Many of his arguments can be found in his On Liberty. He has a famous quote on this:
If all mankind minus one were of one opinion, and only one person were of the contrary opinion, mankind would be no more justified in silencing that one person, than he, if he had the power, would be justified in silencing mankind.
As for some taboo subjects…
Professional scientists fearing advocating for the lab leak theory of COVID-19’s origins, which now has credibility, is a good example. (source 1, source 2)The language in The Lancet statement is chilling and an example of the politicization and moralization of science by scientists.
On February 19, 2020, The Lancet, among the most respected and influential medical journals in the world, published a statement that roundly rejected the lab-leak hypothesis, effectively casting it as a xenophobic cousin to climate change denialism and anti-vaxxism. Signed by 27 scientists, the statement expressed “solidarity with all scientists and health professionals in China” and asserted: “We stand together to strongly condemn conspiracy theories suggesting that COVID-19 does not have a natural origin.”
Doctors and well-respected scientists who questioned the efficacy of lockdowns and wearing masks were canceled and banned from various social media. (source 3, source 4) There’s a general sense among conservatives and libertarians dissent on lockdowns and mask requirements is taboo.
Charles Murray’s research in general and the correlations between race and IQ in particular are very taboo. The book The Bell Curve authored by him and Richard Herrnstein is infamous as it is rigorous in defending a taboo point of view. (source 5, source 6)
The book A People That Shall Dwell Alone is taboo, though was well-received by many scientists. Kevin Macdonald, a professor of evolutionary psychology (now retired), has been heavily vilified for his work, even after distancing himself from misuse of his work.
Much of what Jordan Peterson says is considered taboo. In particular, the treatment of him as well as his ideas solidified the idea that dissent from feminism (mostly third-wave) is taboo in modern Western education systems, though much of feminism is an interpretation, so dissent really can’t be proven incorrect. Antifeminist thought is essentially nonexistent in academia and modern philosophy.
Similarly, many consider disagreement with transgender ideology taboo.
To further address your specification of sociology and psychology, a lot of the politicization of science comes from the heavy ideological bias in social studies, humanities, and academia in general. (source 7,
source 11, source 12, source 13, source 14) This is a general source of what is considered taboo in many fields. As detailed in the sources, many libertarian, conservative, and right-wing beliefs are dead on arrival in these fields, and it’s getting worse over time. Jonathan Haidt writes at length about this. The lack of dissent, unprecedented presence of hegemony, and absence of checks on other researchers’ works and biases has been a source of The Replication Crisis. Some of the previous sources cover philosophy, but it is also dealt with specifically in the following (source 17, source 18, source 19, source 20).
James Lindsay, and Helen Pluckrose in general talk about this issue, often mentioning philosophy. I’d look them up. Peter Boghossian was a professor of philosophy at Portland State University until he resigned due to harassment he received.