I'm fairly certain TEC Loyalists have a -1.35 initial standing towards the Advent Rebels, very easy to overcome. They'll probably have even better standings with the Vasari Rebels.
TEC Rebels have horrendous standings with everyone, such is the price of being a racist aggressive lynch mob that teams up with pirates.
Funny thing is, despite all that, you are more likely to actually go and research some stuff from their Diplomatic Tree than for other factions, thanks to the things like Truce Amongst Rogues, Pirate Mercenaries or the Liberated stuff....