{Desecration demon}+ {Skirsdag High Priest}
Can I activate skirsdag in response to them sacrificing creatures but before the desecration demon becomes tapped
You may not. Once Desecration Demon's ability begins to resolve, it resolves completely. The sacrifice and tap are both done during the execution of a single ability, so no player has priority at that time. You can't respond to the sacrifice by tapping {Desecration Demon} since it will be tapped the next time you have priority to activate the ability of {Skirsdag High Priest}.
This is similar to how you can't {Cloudshift} {Vexing Devil} to save it from being sacrificed.
RESOLVED
Like a boss.
Thank you