I do feel safe saying that Sister Liliya Bogomolova does not care about men. If anything, I think she hates them more than she hates anyone else.
Liliya doesn't kill Dawn. I don't know if she tied Dawn up to the contraption in Despoil the Auction, but she does not cut away at Dawn with her own blade. She uses her voice on Dawn instead, making Dawn want to hurt herself, as all of Liliya’s followers do. That seems to me like she would want Dawn as a follower. In comparison, Liliya does kill the Wounded Reagent with Dawn, a man. There was no attempt to talk to him, to try and convert him, it was just an immediate kill. (Did she want them to be separated?)
There are two sets of dialogue for those in the cages throughout the Resort too. With male Reagents, it appears that she shames them, calls them unclean. Wants them carved. The male Reagent is begging to just understand our dear Sister.
The male Biters are near-universally emasculated, directed to by Liliya. She did the same to her abuser, a man. The female Biters do not appear to be cut near their genitals at all.
Jacque Trégouët, his personal valet, George Nichols, they are all men who fall quickly to her effect. Nichols was traveling with a woman, Domitille. She is not reported to have suffered from Liliya's charms despite having traveled and translated for Nichols throughout his quest. Easterman is majorly succumbing to Liliya's voice but Avellanos has not reported anything like this happening to her. Even Scarfiotti has a line about listening to Liliya's voice, but not Avellanos.
The female Reagent found in the cage simply does not speak in the same way as these guys do. There's more awe to what she's saying; it's not just begging.
The female Reagent could be further along in her brainwashing/worship, but even that makes me lean towards Liliya prioritizing female Reagents/Ex-pop within her service. Not for a good reason. Especially with the mentions of being "still," and to have a "new ingress for unimaginable gods." Dawn was placed in a wedding dress, her body in a display to be sold. Liliya sees Amelia's A and scratches at it (a scratch, an open wound, an ingress: an entrance). I want to be clear, I don't think Liliya likes the women she's targeted either--I think she finds them to be more useful for her goals. I suppose as she's been made useful for her own God. Or she doesn't care. It is however, much more apparent that she views the men in her service as a lesser. They're not being told gods will be entering them. Not by Liliya at least.
