When in doubt, read the rules. It's not hard, they're posted on the AMA web site, and no one is going to demand a quart of blood for the privilege of looking.
This from my copy of the 2013-2014 Control Line General rules:
2. General. A Control Line model is flown on one or more' steel or GSUMP, commonly referred to as
Spectra or Dyneema, lines' steel wire line(s) or metal line(s) of equivalent strength, attached to the model in
a manner providing aerodynamic control of the model’s elevation through manipulation of the control
surfaces during flight.
If you doubt me you're welcome to go look on the AMA web site and read the rules fresh from there.
As far as I know the only competition class where Spectra lines are allowed is combat. This makes sense because combat lines take a beating, and Spectra lines seem to be better able to handle that than steel lines do. Moreover, combat planes often suffer from line breakage, and the combat community has the safety issues relating to that figured out.