Quick answer
Yes. Madeira Airport meets full EASA standards and has an excellent safety record. Pilots flying in must hold a specific Funchal qualification because the approach combines a curved visual to runway 05 with strong, gusty trade winds. Diversions to Porto Santo or Tenerife happen a few times a year in extreme crosswind.
Context
Madeira (FNC, Cristiano Ronaldo International) sits on a single 2,781 m runway built partly on stilts over the Atlantic. The unusual approach to runway 05, a curved visual segment past Ponta de São Lourenço, is what makes it look dramatic on YouTube, but airlines that serve FNC train and qualify their crews specifically for it.
The genuine constraint is wind. Trade-wind days produce strong crosswinds and turbulence in the final approach. When crosswind exceeds the operator's limit, flights hold, divert to Porto Santo (10 min away), Tenerife, or Las Palmas, or return to origin. This is normal procedure, not an emergency, and the live conditions on our airport page show when it's likely.
Statistically, Madeira's accident rate is in line with any major European regional airport. The widely circulated 1977 TAP accident pre-dates the current runway, lighting and approach procedures.