One of the ways that I've learned to practice respect is actually not really getting to know people personally too much. I've been manipulated before by "leaders" who try to use personal information like family needs or other goals as a fake carrot that is not in their power to exchange. As a result I have a pretty "no questions asked" policy on the privacy rights of my direct reports when it comes to approving any time off or facilitating whatever it is they want to do with their careers, and it doesn't require "getting to know them" beyond their own voluntary sharing in private. Sometimes it will grow into a closer relationship but it totally doesn't have to.
Maybe it's an extreme reaction to the bad taste from interacting with folks who like to pretend that work is a family. I just don't trust workplaces enough to be fully vulnerable anymore, and by extension would never demand that another employee be unconditionally trusting with their full humanity, because it is never a two-way street. When the company wants to mess with livelihoods it does not need to seek permission, so it is unfair to ask for the disclosure of personal information beyond what is necessary to carry out the work.
For just one more recent example, I fell for the advertised inclusive corporate culture by putting my pronouns on my Slack profile (having never been publicly out as a queer person at work before), I experienced weird behaviours from people that made it harder to do my job normally. So I ended up going back into the workplace closet because it's just easier to project what "regular" folks want to see in order to solve problems efficiently.
I'd love to hear your take on healthy boundaries, because sometimes I wish there could be more connection with people in the workplace besides the naturally occurring camaraderie that arises through direct collaboration and the inevitable small handful of friends with similar values. Is it possible to have a deeper connection with everyone as a general approach?