When I hear "bring your whole self to work", I think of gay people who couldn't mention their loved ones because that would out them. When you say there should be a "strong separation between your private life", I don't think you're expecting to never mention your family. Maybe your partner is sick and you're feeling stressed. In a supportive environment, shouldn't that be mentioned?

Even though the personal is political (such as the status of being gay), It sounds to me like you're thinking about political topics irrelevant to the organization when you advise people to "avoid controversial and political discussions". Whether the topic is relevant to your work depends on the topic, and it's up to you to make a cost-benefit analysis of whether it's worth discussing. I think that people should be able to discuss their family life and workplace policies, but I agree that broader political discussion may not be worth it.

I guess I'd like to end by saying that it depends. What don't you think should be discussed at work? Why shouldn't you discuss this with your colleagues? Personally, I think discussing a gay spouse should be fine and expected, and supporting genocide shouldn't be, but there's a lot of room in between those two extremes.