Can Mutavault tap for mana and then be animated as a creature on the same turn?

Mutavault has two separate activated abilities: one that produces {1} colorless mana (tapping it as a cost), and one that makes it a 2/2 creature until end of turn (costing {1}). These abilities are completely independent of each other.

Tapping Mutavault for mana does cause it to become tapped, but the creature-animation ability does not require Mutavault to be untapped — it has no tap symbol in its cost. Per CR 602.1, you simply pay the stated cost to activate an ability, and the only requirement is that you pay exactly what is listed.

However, once Mutavault is tapped (after producing mana), it cannot tap again for other purposes — including attacking, since attacking requires the creature to be untapped unless it has vigilance (CR 508.1f). So you can animate it as a creature while it's tapped, but it won't be able to attack that turn.

Concrete example: On your main phase, you tap Mutavault to add {1} to your mana pool. Later in the same turn, you spend {1} to activate its animation ability. Mutavault is now a tapped 2/2 Shapeshifter creature. It cannot attack this turn, but it can block if your opponent attacks on their next turn (assuming it becomes untapped).

This works because CR 602.1 and 602.3a only require you to pay the costs listed on the ability. Since the animation ability's cost is just {1} generic mana, Mutavault's tapped status is irrelevant to activating it.