Will Sigarda, Host of Herons and Armor of Thorns cause infinite cleanup steps?
The sacrifice does not happen; but this does not cause more than one extra cleanup step.


  603.7b A delayed triggered ability will trigger only once—the next time its trigger event occurs—unless it has a stated duration, such as “this turn.” If its trigger event occurs more than once simultaneously and the ability doesn’t have a stated duration, the controller of the delayed triggered ability chooses which event causes the ability to trigger.


This shows that once the delayed trigger happens at the beginning of the next cleanup; it will not trigger again after that. Preventing the sacrifice from happening doesn't change the fact that the trigger still happened.

Sigarda, Host of Herons does prevent the player from having to sacrifice Armor of Thorns, because the controller of the delayed triggered ability is the player who originally cast Armor of Thorns:


  603.7d If a spell creates a delayed triggered ability, the source of that delayed triggered ability is that spell. The controller of that delayed triggered ability is the player who controlled that spell as it resolved.


So there will be a second cleanup step because something triggered during the cleanup step, but there is no trigger that occurs at the beginning of the second cleanup step.