"Master" is a still commonly used term for many technology products. It usually means the primary device or default option. Most modern tech products got rid of "slave" years ago, and replaced it with something like "worker" or "secondary".
Changing "master" to something else that is just going to cause industry confusion, mostly because you'll never get people to agree on what to replace it with. Even if you did think it was a good idea, where would it end... would you advocate changing the 1 or 0 designation in binary code to 1 or 7 or something because people suddenly thought that the number 0 was offensive?
I'm going to ignore the slippery slope aspect of your response.
If your developers are bringing up conversations occuring in the industry, instead of attacking them, why not approach it like a professional?
There is risk that industry naming conventions could cause impact. People on your team are naturally discussing it.
If the naming of your branches are going to screw up your builds, perhaps you should focus on making you processes more resilient and flexible instead of name calling people for bringing up adoption of new naming conventions.
Just to be clear, I do not agree that naming conventions need to be updated to remove "Master" nor does it concern me that there is a push to remove it.
Naming conventions, standards and industry practices change. Reserved words change.
What matters is being able to respond to change