Yes, it is permissible to make wuḍu while naked, such as after bathing, and the wuḍu will still be valid. Covering the ‘awrah (private parts) is required for Ṣalah (prayer), but it is not a condition for the validity of wudu itself. Therefore, if someone finishes bathing and then performs wudu before getting dressed, their wudu is valid.
However, Islam encourages modesty and covering the ‘awrah whenever possible, even when alone. The Prophet ﷺ said: “Allah is more deserving that you feel shy before Him.” (Sunan Abu Dawood). So while wudu without clothes is allowed, it is better to maintain modesty if possible, especially when others may be present.
O Allah, purify our bodies and hearts, accept our worship, and keep us firm upon modesty and faith. Ameen 🤲
And Allah knows best.