If using a different term for something makes your coworkers feel less uncomfortable at work, then absolutely. I've got no problems changing terms. But it's unclear to me that this change in terminology is actually driven by uncomfortable employees rather than management overreacting to the current political climate.
But I'm also a privileged straight white dude. Any black people in here want to weigh in with their feelings on the black hat/white hat thing? Is this a real issue?
I'm also a white dude, but I can give you a real-world example of how these terms made everyone on my team uncomfortable.
Quick background - I'm a scientist that's forced to code, instead of a coder who works on science. I'm pretty low on the coding spectrum. For the last 3 years I've been working on a coding project to take environmental and fisheries data, model it in near-real time and use that to produce a suite of graphics which help managers set catch limits and for the fishing industry to know the status of the stock.
Anyway, there's nine of us in this group, let by two genuine coders who know little about ecology/biology and 7 biologists that stumble their way through writing code. For the rest of the post I'll use "main" and "branch" - our currently preferred terminology, but these are akin to the former "Master" and "Slave".
On any given month each of us is working on a 'branch' of the 'main code, with the two dedicated coders overseeing the 'main' code (because that's what they are good for and because they have definite blindspots when it comes to understanding ecological data in context). For example, I spent several months on a branch that could import data from several dozen buoys (e.g. temperature, wind, swell), error check it, and apply a running 24h average and then feed it into another branch that dealt with developing a 2D spatial model (much like those colorful weather maps you see on the news).
When I first started the two coders still used the traditional terminology of 'master' and 'slave'. To keep everything together and allow people to see who was working on what we use software that lists who is working on what, as well as a white-board for our weekly meetings. Basically it would say "nereo - slave, weather". Now it's "nereo - branch weather" (and it's DONE!! so I'm on a new branch...)
Several of us were not comfortable with this, and we discussed migrating to different terms. At the same time, we had a new postdoc join our group who was black, and was also new to coding. Everyone became uncomfortable, as no one was going to write "Nicolas - slave [name of branch]". He's my friend now and I can say he would not be cool with it either.
All ofnthis was occurring just over a year ago and coincided with GitHub's move to change those terms. So one meeting the head coder asked about changing the nomenclature and we unanimously agreed, some of us very enthusiastically.
Besides just giving you a real world example, the other reason I share this is to emphasize that - for people who have been coders most of their adult lives - the terminology is embedded and second nature. With familiarity comes acceptance, or at least a sort of blindness to why others might cringe at its usage. For the rest of us, who were/are just dipping our toes into the world of coding, it was uncomfortable. As the terms weren't ideal to begin with shifting made sense for us.