Can you opt out of the Fated raid affix?
My guild and I are rounding some participants up to take on non-Fated Mythic Sylvanas Windrunner in Sanctum of Domination for a shot at the https://www.wowhead.com/item=186642/vengeances-reins mount. We're in a bit of an odd situation, though, as Sanctum of Domination will be the Fated raid in a couple weeks, and there are plans to make https://www.wowhead.com/guides/fated-raid-affixes-shadowlands-season-4 , which means the difficulty will be on par with current-content Mythic, which not all of us are geared for (we're all kind of in a "Dragonflight waiting room" mode, so not all of us are geared to the teeth).
What would be great is if we could turn off the Fated affix for the raid when it's Sanctum of Domination's week to be Fated, and we could run through the raid at reduced difficulty. I noticed at the start of each raid there's now a "Fated Console" but interacting with it https://us.forums.blizzard.com/en/wow/t/additional-fated-power-in-season-4-fated-raids/1335654 , which isn't what I'm looking for.
Is it possible to opt-out of the Fated affix when running a Shadowlands raid?
Short answer is no, not at the moment.
The wowhead page you linked is up to date with the current state of the game, and nobody knows whether or not fated will be able to be toggled after the rotation is removed in the future, as to my knowledge no official announcements have been made regarding the details of that change thus far.
Here is the actual fated schedule blue post from blizzard which sites like wowhead are referencing: https://us.forums.blizzard.com/en/wow/t/season-4-fated-raid-schedule/1285146
Relevant excerpt to your question:
While a raid is Fated, it will only be available in Fated difficulty, but the other two raids will still be available that week in their non-Fated difficulty.