Can a creature with vigilance still be tapped by an opponent's spell after it attacks?

Vigilance (CR 702.20) means the creature doesn't tap when it's declared as an attacker. That's the full extent of what vigilance does — it removes the default rule (CR 508.1f) that taps a creature when it attacks.

Vigilance provides no protection against being tapped by external effects. If an opponent plays a spell or activates an ability that taps your creature — such as Icy Manipulator or Opposition — your vigilance creature can absolutely be tapped by those effects, just like any other permanent.

This matters because a tapped creature, even if it has vigilance, cannot block (CR 509.1b). So an opponent can use a tap effect after you attack with your vigilance creature to prevent it from blocking on a subsequent turn, or to neutralize it in other ways.

Example: You attack with a 3/3 creature with vigilance. It remains untapped after attacking. Your opponent then activates Icy Manipulator, targeting your vigilance creature and tapping it. Your creature is now tapped and cannot block this turn, even though vigilance kept it untapped through combat.

Bottom line: vigilance is specifically about the attack declaration step only. It offers zero protection against spells, activated abilities, or triggered abilities that tap permanents.