>But we don't really have IC data to not trust them
Actually, yes we do.
1. They employ Orochimaru, known S-Rank internationally wanted rogue ninja, who has a reputation of performing illegal and banned human testing.
2. They also employed Deidara, who murdered an important Hidden Stone shinobi in order to steal her Forbidden Technique.
3. Their ranks, until the alliance with the Mist, Leaf, and Stone, were composed of unknown and rogue ninjas.
And even if the ability that Satori is using is some kind of passive effect, that only means that he has a kekkei genkai to Shimaru, and should be treated with suspicion.
Shimaru's coldness towards Akatsuki derives from their reputation and the quite possible inevitable betrayal.
There's also the difference between Shimaru, a professional, and Satori, an idealist. Shimaru can get along with other shinobi, such as the Konoha ones like Might Guy, Kakashi, and Asuma because they're also professional mercenaries like himself. But Satoris is an idealist leader, the kind that use mercenaries and professionals, without being one himself. That's not to say that Satori isn't a strong fighter himself, just that he's not another professional.
Finally, as to the dinner.
Bringing Gen and Aya would be a social misstep. Gen, while he might have worked on the seals for the Swordsmen's swords, isn't a member of the team. Even more so for Aya, who's in Intelligence as an analyst. If everyone had just finished working on some big project together, then it would be acceptable, but you're just forcing everyone together for your own selfish reasons and socially this only makes an awkward situation.