Does Magus of the Moon affect Urza lands that are already tapped for colorless mana?

Magus of the Moon (and Blood Moon) changes all nonbasic lands to Mountains, which means Urza's Mine, Urza's Power Plant, and Urza's Tower lose their printed land types and abilities and gain the Mountain subtype and the basic Mountain's mana ability (tap to add one red mana). This is a continuous effect governed by CR 305.7 and the layer system (CR 613).

If a player already tapped an Urza land and the mana is sitting in their mana pool, that mana is unaffected — mana already produced is not retroactively changed (CR 106.4). The mana ability resolved and produced its effect before Magus entered the battlefield or before the relevant state was reached.

Going forward, however, the Urza lands are now simply Mountains. They lose the linked abilities that let them tap for extra colorless mana when all three Urza lands are in play (CR 607, linked abilities). They can only tap for one red mana each, just like a basic Mountain.

Concrete example: You control Urza's Mine, Urza's Power Plant, and Urza's Tower. You tap the Mine for {C} and put it in your mana pool. Your opponent then casts Magus of the Moon. The {C} you already produced stays in your pool. But when you tap Urza's Tower, it is now a Mountain and only produces {R}, not {C}{C}.

So: mana already generated is safe; all future activations of the Urza lands under Magus of the Moon produce only {R} as basic Mountains (CR 305.6, 613.1b).