Show Varys and Book Varys are two different creatures. I have no problem with show Varys and his motives are not complicated in any way by supporting a Mummer’s Dragon.
Book Varys, otoh, has yet to show his true colors and motives. There is not a chance the Aegon is a real Targ. We know this to be true with reference only to the facts as set out in the book as Illyrio reveals that Viserys was their first choice. That cannot be if Aegon was a real Targ as Aegon’s claim is clearly better than Visery’s claim. Moreover, Aegon was a supposed Targ heir who was wholly within their control and is by all accounts a decent and reasonable young man who is comfortable believing he is a royal Targ. Yet they chose Viserys as their first choice. Nope. Viserys can’t be their FIRST choice if Aegon is real.
The fact that Aegon has been completely omitted from the show further underscores the fact that he must be false, introduced by GRRM principally as a red herring and to muddy the waters of his prophecies, who the false dragon is, who the Prince/Princess who was Promised is as well as who the Three Heads of the Dragon are, in truth. Those motives GRRM has to keep the prophecies cloudy are not concerns that the show has, as the show has completely ignored almost all of the book’s prophecies. Hell, it’s even ignored the ONE prophecy the show actually made (Balon Greyjoy’s fate has not been shown - and that one was explicit on the show, damn it) while leaving the introduction of part of Cersei’s prophecy to the beginning of Season 5.
So no, “Aegon” must be descended from, at best, a Blackfyre bastard who they deceived Connington about as their “iron in the fire” in case something went wrong with Viserys and Dany. Well, Viserys died – and Dany slipped beyond their control. Rather than try to devote all their resources to Dany to bring her back under their wing, the only bone they throw her is Tyrion – mainly as a way to influence her should she somehow emerge from the East. And maybe they will marry her off to Aegon (except Tyrion messes that up by putting ideas in Aegon’s head).
Instead, they throw all their material support behind the pretender, Aegon - a false Targ.
So the idea that Illyrio and Varys are all about a true Targaryen restoration for its own sake is clearly false. Book Varys has other motives, and they go beyond mere temporal power and influence – though that is clearly part of it. Backing Aegon in preference to Dany (or any other claimant) suggests there are other motives behind Varys’ game – and we simply don’t know what they are yet.
My guess is that there is some religious motive, or at least their opposition to magic which has something to do with what they are all about. A motive which is satisfied as long as “Aegon” is a bastard with some of the Dragon blood in him.
Whatever the heart of it is, in the books, we don’t know the whole of it yet.