Pyromantic Pilgrim

Haste is a static ability.

If a creature has haste, it can attack even if it hasn’t been controlled by its controller continuously since their most recent turn began. (See rule 302.6.)

If a creature has haste, its controller can activate its activated abilities whose cost includes the tap symbol or the untap symbol even if that creature hasn’t been controlled by that player continuously since their most recent turn began. (See rule 302.6.)

Multiple instances of haste on the same creature are redundant.