Varys Has Always Been About the Bigger Picture
When we first meet Varys, he's a complete mystery. Is he one of the bad guys or is he fighting for good? Does he want the Iron Throne for himself or is he working for someone greater? Is he a merman or nah? The things we do know about him are subject to scrutiny: he's been the Master of Whisperers for a couple of sovereigns who all die in some really messed up ways; he knows everything that's going down in the Seven Kingdoms , as well as outside of them; he has his hands in all types of pies; and his spies are poor children known as Little Birds. Seems super sketch from the get-go.
But, as we learn as the series progresses, Varys' main goal has always been to protect the realm from unfit rulers. Everything he's done has been to manipulate those in power to do right by the people they're supposed to serve. He has no loyalty to Houses and doesn't really care who he has to get rid of to get the job done; his loyalty is to the entirety of the known kingdoms of Westeros. Unlike a majority of the characters on GOT, Varys has always been here for the bigger picture — the welfare of the kingdom rather than his own needs and desires.
This is why he buys into Daenerys's hype for so long. As the Breaker of Chains, she genuinely seems to want to be the benevolent ruler that Westeros desperately needs. He's seen how the people suffer under the hands of men obsessed with power and a woman who fights for slaves is infinitely a safer bet.