Can a Monk take Racial Paragon levels and then take Monk levels again without taking the feat for that?
Racial paragon classes don't have any special exemption clauses for Monks or Paladins, and despite their short length are treated by the game as being base classes, as demonstrated here by the SRD:
Though racial paragon classes call out a specific exemption from multiclassing XP penalties (a godsend, by the way, for anyone interested in them), nowhere in their description (here) do they call out an exception to the multiclassing rules for Monk and/or Paladin.
Your DM is able to/should most definitely house rule away the multiclassing rules on Monk, but by RAW, them's the breaks.
No rule book handy but from memory.
Barring a specific exemption in the class ( which it obviously doesn't have or you wouldn't be asking) or a feat that allows it, no.