Does wearing nail polish or gel nails invalidate wudu?

Yes, in the mainstream classical view — ordinary nail polish forms a water-impermeable layer over the nail, and since wudu requires water to actually reach and cover the nail surface, wearing regular polish (or gel/acrylic nails, which have the same water-blocking effect) prevents the wudu from being valid until it's removed. This is a shared position across the madhabs, not really a point of classical disagreement — the issue is physical (does water reach the nail or not), not a difference in legal reasoning between schools.

Newer "breathable" or "wudu-friendly" nail polishes marketed as being permeable to water and air have generated real contemporary debate: some scholars and fatwa bodies have accepted specific tested products as valid for wudu on the basis that they genuinely let water reach the nail, while many others remain cautious, since verifying actual water-permeability isn't straightforward for an ordinary user and product claims vary. Given that uncertainty, the safest and most widely recommended approach — especially with standard, non-breathable polish or gel/acrylic nails — is to remove it before wudu and ghusl, or to plan around prayer times if that's not immediately possible.

Source: general fiqh on substances that form a barrier to water reaching the skin/nail during wudu and ghusl; contemporary fatwa discussion on "breathable" nail polish, e.g. Dar al-Ifta and IslamQA.