The other essential part of not mentioning politics at work is that these private beliefs should not impact work conduct.

EG as per a sibling comment, if an HR Rep is not convinced regarding trans-rights, they should absolutely not let that impact their treatment of a trans person that comes to them.

Or, more famously, (and not that it did him any good) Brendan Eich made a political donation to candidates opposing gay marriage, but (afaik) there were never any reports of him mistreating any LGBTQ+ employees.