Good questions, Zaf.
Vito initially opposed the drugs business. But as you know, he agreed to provide police and political support in order to bring Michael back from Sicily safely. So, you might argue that Michael was simply continuing his father's policy.
But it isn't clear to what extent Michael was involved with drugs after Vito died. He whacked all the Dons (including Barzini and Tattaglia, who backed Sollozzo). But we don't know if he simply folded the drugs business or (more likely, IMO) continued to protect the business and take a cut of it through Clemenza and later, Pentangeli. Frankie protests to Michael re. the Rosato brothers that "everything with them is women, broads, and
a babania, junk. An' they leave the gambling to last." That statement doesn't necessarily mean that Frankie, functioning as a caporegime under Michael in NYC, had no involvement in drugs and prostitution--I take it to mean that the Rosatos were
neglecting his main business--gambling. When Tom tells Michael that Frankie ratted him out to the cops, he says, "They had him on Murder One,
possession.. (emphasis added). "Possession" could mean drugs--or it could mean some other illicit stuff, like guns.
To net that part out: I doubt that Michael would walk away from money-making illegal businesses in NYC.
As for the Nevada brothel that Fredo operated: Prostitution was never illegal on a statewide basis in Nevada, and Fredo's brothel was legal. Not moral, maybe, but legal. Gambling was legal, too. Since Michael intended to be "legitimate," he was in "legitimate" businesses.
As for labor unions: They are a rich source of money for organized crime in the US. They could be trade unions, craft unions and even public employee unions, but the
modus operandi for the Mob is still the same. They dominate union locals by forcing their own men into leadership positions. Then they plunder unions' rich treasuries (dues, pension funds, etc.). They use unions to provide support for Mob-friendly politicians (money, voter turnout). They also extort contractors--if the contractor doesn't pay off the Mob, unions working on his site can cause a slowdown or even a strike that will cost him dearly. Unions were a very, very rich source of money and influence for Vito, and presumably, Michael. One of the reasons Vito may have had all the judges and politicians in his pocket was that the unions he controlled through his own men would steer campaign contributions and votes to them (judgeships are often elected positions in the US).