Hudson was responsible as director of the ME trilogy. Gameinformer interview where a Bioware art director clearly states the Asari were meant to be beautiful women, space babes like in Star Trek and Star Wars. https://www.youtube.com/watch?v=L2IcNQktHIs
Shepard can threaten and execute men, while saving women. Essentially every female squad mate is recruited by saving her. Ashley is running away from enemies. Tali is being groped by some male alien. And Liara is suspended in a trap, literally calling for rescue. Then there is the doctor early on. She is saved from thugs. Later on Ferros a male character is holding yet another female character hostage. Scantily clad women and Asari dance on tables and poles in every game of the trilogy. In ME3 female companions have very visible breasts and bodies even in armor. Edi's robot body is basically naked. Of course if Kaidan is dead and if a Garrus romance was not imported from a save, FemShep is left with no romance options in ME3.
And of course ME1+2 had lesbian content. There were so many romance options in ME2, yet not a single one was available to gay Shepards. Not even a flirting options. Shepards just could not possibly be gay. And then Hudson made some bullshit excuses in interviews why it wasn't possible. Obviously the Mass Effect team, as opposed to the Dragon Age team, didn't care to invest any ressources in anything gay or they didn't want to offend homophobic players.
Even the self-declared queer-friendly Patrick Weekes wrote the sex scene is the centerpiece of Samantha Traynors romance. That may be because the whole romance is barely 3 minutes long. Her male equivalent Steve Cortez has no sex scene. Instead he will ask ManShep again and again if he wants to be homosexual.
As to what this means for Bioware games it would appear to be good at first place. Apart from the points above the ME trilogy was pretty good. Except Hudson was both part of Andromeda's initial pre-production team where big open worlds were already decided, and before he left the company he was the lead on Anthem, Bioware's new open world shoot and loot multiplayer, which still looks like Destiny or the Division more than a story-rich RPG.
So I am not too optimistic. If I recall correctly, Aaryn Flynn was at EA first before he joined Bioware. He supervised the transistion to Frostbite and open world or open level games Inquisition and Andromeda after the original Bioware founders left after ME3 and SWTOR. I'm unsure whether it was EA, Bioware or both who wanted to get in on the Skyrim, Witcher, Assassin's Creed open worlds with less story. Who knows if the faults of Inquisition and Andromeda lead to not just to a new general manager but a change back to what Bioware was good at.