BUR #50781 has been approved by @nonamethanks.
create implication female_producer_(idolmaster) -> producer_(idolmaster)
No one seems to have addressed how the Female Producer (Idolmaster) should work yet (I guess because it's extremely small). Currently it's mostly getting applied at the same time as the Producer (Idolmaster) tag, but without an implication.
There's no consistency in how gendered versions of the "generic nameless protagonist" are dealt with in various other copyrights.
The Kantai Collection wiki states that the default Admiral is male, and Female Admiral (Kancolle) does not imply Admiral (Kancolle). Girls' Frontline is the same, Female Commander (Girls' Frontline) is separate and doesn't imply the main tag.
For Blue Archive, Umamusume, and Azur Lane, the female tag implies the main tag, and there's no male tag.
For Path To Nowhere, Touken Ranbu, and Arknights, there's separate female and male tags that both imply an ungendered umbrella tag (this is probably because Path To Nowhere and Touken Ranbu are unique in that the female version is much more popular than the male, and Arknights is unique in that the player character has their face covered by a mask and is usually depicted without a gender).
The middle approach is what I think makes the most sense as a default when the player character is mostly depicted as male. So that's what I'm suggesting for Idolmaster.
