My thoughts on the Spider, and this is just me spit balling from what I know of the show...
Varys has been on the level describing his past. The troupe of actors and mummers the whole bit. He was gelded, root and stem and left to die. He rose in the world of shady deals and thievery, discovering that being a master of secrets was more profitable and less labor intensive than going out and actually stealing himself.
I want us to put ourselves in the shoes of a man that had such a vital part of life taken from him and then was left for dead. I think that Varys is no idealist but he also has great wells of empathy. He sees things others don't since the distractions of family and sex ect. are more or less theoretical to him and don't hold the power they do over others. Can he be cold blooded? Absolutely. But he isn't just a cold hearted SOB. He knows what it's like to be weak and be preyed upon by the powerful. If he takes interest in a conflict it's because he is looking in some way to aid the side that will in the long run do the least harm and the most good for the weak and oppressed of Westeros. He doesn't let idealism blind him in any way. LIfe's lessons to him have been harsh. He, however, can't stand by and see only senseless destruction, waste or cruelty descend on the masses. There's part of me that thinks he was scheming to take out the Mad King himself before the King's own excess and insanity did the job for him.