No. Enchantment is not a creature type; it's a card type, like 'creature'. The creature types are subtypes of the card type creature. Enchantment is on "another level" so to speak.
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I'm a former judge (lapsed), who keeps up to date on rules and policy. Keep in mind that judges' answers aren't necessarily more valid than those of people who aren't judges; what matters is we can quote the rules to back up our answers. When in doubt, ask for such quotes.
Mutavault itself will not become an enchantment when you make it into a creature. It will have the types Creature Land, and then every creature subtype.
W may only be paid with white mana. U may only be paid with blue mana. B may only be paid with black mana. R may only be paid with red mana. G may only be paid with green mana. C may only be paid with colorless mana. 1 may be paid with white, blue, black, red, green, or clolorless mana.
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