Is it racist to use the term 'Master Bedroom'

That change of wording doesn’t change anything. Offence is already a tenuous concept, “uncomfortable” is even more so. Even more things rise to level of causing people to feel uncomfortable.

The person who uses the the word retains the option of using/not using.

The person who has the non-offensive context/usage/intent explained to them has the option to continue taking offense/feeling discomfort or not, or even to try to get comfortable with hearing it in future.