It depends on what your trying to do exactly, but I believe that yes Vice is necessary to further her corruption at least to the final level. If you're going for as lewd as possible though I wouldn't kill the worshipers, there's tons of Lewd events there.I tried to search through most comment but the 231 pages of comments didn't help.
I'm currently at the start of chapter 2 and the max lewdness guide really want me to gather those vice stats, I'm currently at 0 vice and day 47. The guide also want me to kill worshiper at the underground rather than building trust to do it the way I want but this game confuse me more and more as I play it ...
Is vice obligatory to go further in Aura's mind corruption ?
Also, does vice lead to Aura being less submissive ?
I'm so confused about this stat, I don't want to do criminal activities with Aura ...
Vice does NOT make Aura less submissive, think of it like advanced corruption. Vice is major immoral behavior like stealing, corrupting innocents, killing innocents, and condoning slavery. My corrupt Aura stole, corrupted, and had a sprinkling of slavery, but never murdered.
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I should also mention that if you get corrupt and cursed enough, you'll take the vice option if you want to or not.