I would count this claim as exaggerated. The context for it rests in the movement among some realtors to refrain from using the term "master bedroom" because of its slavery-related connotation, according to Caitlin O'Kane's 2020 article for CBS and Sydney Franklin's 2020 article for the New York Times.
Some realtors no longer using "master" to describe bedrooms and bathrooms - CBS News
The Biggest Bedroom Is No Longer a ‘Master’ - The New York Times
While Zillow nor Redfin specifically have a "master bedroom" search category or any allusion to the term on their sites, I feel that it is important to note that the descriptions of the homes on these sites are written by realtors, and so the presence of or absence of the term "master bedroom" comes down to the individual realtors' sensibilities. As a test, I looked up "house with huge master bedroom redfin" on Microsoft Edge and a result for a realtor-written description including the phrase "master bedroom" did populate.
1906 Brimberry St, Houston, TX 77018 | For Sale ($499,999) | MLS# 30263138 | Redfin
Finally, I looked into Michael Aloysius, the Bluesky user who originally posted this statement. In his feed, I see that he has defended the Trump Administration from criticism from another Bluesky user, and he has also complained about the lack of right-oriented (i. e. politically conservative) users on the platform. Considering this, Aloysius may be reactively exaggerating the reach of a movement seen to be of liberal origin, as much of the push to replace the term "master bedroom" came as a response to George Floyd's death in 2020, according to Franklin in the New York Times.
The Biggest Bedroom Is No Longer a ‘Master’ - The New York Times
Ultimately, it is true that some realtors have stopped using the term "master bedroom." However, there is no evidence to suggest that Zillow and Redfin have specifically stopped using this term, especially because much of their content is independently generated by realtors. Lastly, this claim was made by someone likely to oppose the movement against the term "master bedroom" because of their own political leanings, meaning they would have a motive to exaggerate this claim.