I disagree completely. It would be entirely out of character for Dedra Meero to storm out of a room just because of a "mansplaining." And if the writer wanted to show an Imperial patriarchy, it would have done so from the beginning in any one of her earlier interactions. A show that isn’t written as well would use the depiction of a patriarchy as a shortcut for "Empire bad." This show is a lot better than that.
If anything this show actually describes the Empire as quite egalitarian. They make a point that the structure of the Empire creates bureaucrats who are more interested in career advancement than overall efficacy. Dedra's reputation for ingenuity is why she was brought into the ISB and why she started to make waves. She stepped outside of protocol by running her investigation of stolen tech outside of her jurisdiction into other sectors. Naturally the other ISB supervisor, Blevin, interpreted this as an attempt to usurp control of one of his six sectors because, in his experience, that is exactly what career-minded bureaucrats do. This led to the confrontation where he accuses her of going "rogue" (pun intended?) but she takes the opportunity to describe and criticise the weakness of the system that, she believes, are being exploited by an occult rebellion. There is nothing about that exchange that suggests Blevin might be attacking Meero because of her gender. She was attacked for disturbing the status quo. It would have been no different if she was male. And Lt. Meero is actually favored for her enterprise despite being the newcomer.
My initial read of her response to Lonni was that she might have thought he was being another competitive bureaucrat, like Blevin. But I thought it was strange that she left the room. In my next viewing, after I knew he was a rebel mole, I can see that his suggestion to have the Empire investigate would be a tipoff to cancel the planned raid on the power station because of the added Imperial scrutiny. Lt. Meero is adept enough to notice this and it sparked her suspicion of him. She probably left so she can start investigating Lonni.
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I, too, was surprised she let Syril go on the way he did. I think she was initially just in disbelief but, as he was talking, she wasn't looking directly at him. I think the wheels in her head had her thinking of ways she could use Syril and his fanaticism as a tool.
I disagree with folks who say they are similar. They are distincly dissimilar. Syril, with his overbearing mother, has something to prove. Dedra has nothing to prove. Her actions are devoid of ego. For Syril everything he does is dictated by his ego.