My internal model of academia is that (1) as a group we are one of the most tolerant of biological and philosophical differences (e.g., gender, sexual orientation, and religion) and (2) that we are likely to take extreme views on issues related to our research. I have no evidence for either of these and they seem potentially at odds in that it seems strange that people would be so passionate about their research and be blase about their religion (or any other philosophy). Is there any work that characterizes the level of tolerance of academics on various issues?
There is a recent study which generated quite a bit of noise and seems to indicate that racial and gender biases do indeed exist in academia (at least in the U.S.). The researchers sent e-mails to professors pretending to be a prospective graduate student, and response rates varied widely depending on the ethnic- and gender- markers in the purported student's name.
As a matter of fact, academics tend to be quite left-leaning, especially in fields like sociology. (Here's an article about this, with links to multiple studies.) Sadly, they're not abnormally likely to be tolerant of conservative viewpoints.
David French is the president of the Foundation for Individual Rights in Education, a nonpartisan group that monitors free speech on campus. In a 2005 interview with ABC News, French argued that "the universities have been so captured by the left point of view, that you're going to get more political and intellectual diversity at your average suburban mega-church than you are at an elite university." The cause, he believed, was the systematic suppression and censorship of conservatives.
That same year, Rothman, Nevitte and Lichter published a paper using data based on a telephone survey in 1999 of approximately 4000 faculty, administrators, and students. The purpose of this study was to test if professional advancement is influenced by ideological orientation. What they found out, was that conservatives and Republicans taught at lower quality schools, compared with liberals and Democrats. This suggested, they argued, "that conservative complaints of the presence and effects of liberal homogeneity in academia deserve to be taken seriously".
A 2014 study by Iyengar and Westwood underscored how powerful political bias can be. In an experiment, Democrats and Republicans were asked to choose a scholarship winner from among fictitious finalists, with the experiment tweaked so that applicants sometimes included the president of the Democratic or Republican club. Four-fifths of Democrats and Republicans alike chose a student of their own party to win a scholarship, and discrimination against people of the other party was much greater than discrimination based on race.
For a 2016 study, Shields and Dunn surveyed 153 conservative professors. “As two conservative professors,” they wrote in The Washington Post, “we agree that right-wing faculty members and ideas are not always treated fairly on college campuses. But we also know that right-wing hand-wringing about higher education is overblown.” Nevertheless, about one-third of the professors professors admit to using "coping strategies that gays and lesbians have used in the military and other inhospitable work environments", ie they "closeted" themselves by passing as liberals. Some also said they were badly mistreated on account of their politics.
In a 2017 speech before the Stanford Board of Trustees, former Provost John Etchemendy argued that he "watched a growing intolerance", "a political one-sidedness, that is the antithesis of what universities should stand for". "It manifests itself", he argued "in the intellectual monocultures that have taken over certain disciplines; in the demands to disinvite speakers and outlaw groups whose views we find offensive; in constant calls for the university itself to take political stands".
In 2009, world–renowned political scientist Norman Finkelstein was denied tenure at DePaul University for his criticisms of Israel's human rights violations against the Palestinian people. In 2014, co-discoverer or DNA James Watson was forced to sell his Nobel prize after losing most of his income for stating that people of African descent are less intelligent than white people. In 2017, graduate student Lindsay Shepherd was hauled before a three-person panel at Wilfrid Laurier University, which interrogated her for more than 40 minutes for showing a first-year communications class a video snippet from TV Ontario of Jordan Peterson debating another professor on the use of gender pronouns. In 2018, University of Pennsylvania Law School professor Amy Wax was removed from teaching mandatory first-year courses for saying in an interview that she didn't think she'd ever seen a black student graduate in the top quarter of the class.
These are some of many examples where academics / scholars have been reprimanded for making statements deemed too "politically incorrect" by their employers. While such cases are obviously but annectodal evidence at best, they do suggest Etchemendy may have had a point when he said he watched a growing intolerance "that is the antithesis of what universities should stand for". They do suggest it may indeed be safer for conservative professors to pass as liberals. They do suggest that French may have had a point when he argued there was systematic suppression and censorship of conservatives. And they do suggest that Rothman, Nevitte and Lichter may have been right to conclude that that conservative complaints of the presence and effects of liberal homogeneity in academia deserve to be taken seriously.
I think it might depend on the field. For example, if you are in a Biology department, you're likely to be labeled as "ignorant", "dumb", or "coward" if you are Christian (or Jewish, or Muslim or any religion that believes in a God who creates), regardless of whether you believe in evolution or not, and regardless of what your actual religious beliefs are. Generally, in natural sciences that's a pretty common trend I think. One could argue that this is more related to the second point you mentioned, rather than the first one, but given that this intolerance, as I said, is regardless of the opinion of the religious person about the origin of life and rules of physics, one could also argue that having this opinion that "any religious person is incapable of appreciating science" as an assumption, is a form of intolerance.
(There is a documentary about Christian professors in science (or biology) departments who were not tolerated by their colleagues and were discriminated against, but I couldn't find it now)
When it comes to ethnic and racial tolerance, in my experience, a level of racism and orientalism that would face condemnation in the US (but not necessarily in Europe) is not uncommon in academic communities in Europe. That being said, my impression is that they're still considerably more tolerant than an average person (or at least an average conservative) in that society.
But overall, I perceive academics to be more tolerant than the median member of the society.