In both Breaking Bad and Better Call Saul, Gus is shown to be a master at disguise and deception.
In private, he is cold and psychopathic: he remorselessly ordered Mike to kill Werner, he brutally killed his long-time henchman Victor just to send a message to Walt and Jesse, and he is strongly implied to have ordered the murder of a young boy. However, in public, Gus is able to fully mask the darkness within him. He is extremely kind and pleasant to everyone, and even hosts charity events and fundraisers for the police and the DEA. His disguise is so flawless that no one suspects a thing about him.
Imo, his ability to hide his true self could very well originate from the need to hide his homosexuality. Gus spent his childhood years in 1960s Chile, a deeply conservative society where homosexuality was illegal. This worsened when Augusto Pinochet took power in 1973, when Gus was ~15. Queer individuals were subject to violent repression during this time, and were even sometimes sent to state detention camps. Because of this, Gus would've had to hide his homosexuality at all times in order to avoid the rampant social and legal consequences that would come if he came out or was caught having relations with a man.
Another thing worth mentioning is that despite the immense repression under Pinochet, it was during this time that the first queer organizations in Chile emerged, though their activities were of course carried out in secrecy. If Gus was involved in an underground organization like this in any capacity, this would've given him experience concealing not just his own illegal activities, but those of an entire group. This experience would've helped him immensely when he eventually became a drug distributor for the cartel, as he would've once again had to avoid the ever-present eye of the government. It's already implied that he held a role in Pinochet's government/military, so maybe he was double dipping as a public oppressor and secret liberator, or maybe he started out as a liberator but eventually became an oppressor.
In conclusion, Gus has such a good ability to hide his true self and his criminal activities because imo, he's been doing it his entire life.