There are true statements that are rightly unacceptable because placed in certain rhetorical contexts, there's an implied argument that they're making which has been rejected by society.
For example, JK Rowling's statement that "there used to be a word for people who menstruate" was essentially true (menopause aside), but had a hefty implied message about the legitimacy of transgender women, one which is rightly considered offensive to most of modern society.
Edit: Since people are nitpicking, here's an even starker example: Can you imagine contexts where it would be rightly offensive for an African-American to be told the true statement "My ancestors used to enslave people like you"?
For example, JK Rowling's statement that "there used to be a word for people who menstruate" was essentially true (menopause aside), but had a hefty implied message about the legitimacy of transgender women, one which is rightly considered offensive to most of modern society.
Edit: Since people are nitpicking, here's an even starker example: Can you imagine contexts where it would be rightly offensive for an African-American to be told the true statement "My ancestors used to enslave people like you"?