In addition to what was said about Berman, there’s also Gene Roddenberry. The best way I can explain how his opinion of women evolved over time is that he allowed Marina Sirtis to have that role on TNG even though she didn’t sleep with him. The same was not true of Nichelle Nichols in the 1960s.
Sirtis only stayed on the show after season 1 because Denise Crosby left. Not because there was a rift between them, but because she wasn’t crossing the “too many women on the show” threshold anymore.
Gates McFadden left TNG for Season 2 because she ran afoul of Maurice Hurley, one of Roddenberry’s lap dogs:
I had been in conflict with one of the male writer-producers about certain things I thought were sexist. What I’ve heard is that he said ‘Either she goes or I go.’ I was shocked that they let me go, because I knew my character was really popular. But he was going to be writing more and more and didn’t want to have to deal with me. What was great was they got rid of him and asked me to come back.
To his credit, Rick Berman asked her back, but I think it was only because Dr. Katherine Pulaski was such an unpopular character and the fans kept writing letters about bringing back Dr. Crusher.
Rick Berman and Gene Roddenberry understood, to varying degrees, that it was important to have women represented as strong, intelligent equals—but did not necessarily personally hold that value.