You fall for any (willing) evil act, but you don't fall for a chaotic one unless your alignment changes
Thay have to "respect legitimate authority". Questions of legitimacy gives you a lot of wiggle room, particularly if you consider that the ruler is still bound by both law and custom. Even if you can't work find reason to consider the authority illegitimate, respect does not necessarily require obedience. Fundamentally, Paladins need to remember that they serve an authority higher than that of any mortal rulers.Paladins need to obey local authorities.