There is very little scholarly research about unions and organized crime according to an article and book I found on the topic. At this point the topic now seems unimportant because unions have been in decline in the USA and the mafia largely lost control over unions by the 1990s. The book said that the US is the only nation in the developed world where unions were repeatedly infiltrated by organized crime and it argues that that is one reason why the US is less unionized than most rich nations. All of the scholars agreed that mafia involvement was bad for unionization because the mafia makes money by extracting money from the unions and extorting businesses. They essentially taxed the unions which reduced union efficiency and reduced the benefits of unions for workers and reduced union jobs and increased opposition to unionization.
For a popular-culture example of how inept the mafia was at running a productive organization, see the award-winning film, The Irishman, which is allegedly based on actual events. It portrays the mafia as a bunch of inept thugs and mafia involvement was politically disastrous for unions because it helped turn public sentiment against unions in the US. If you do a Google search for unions, you will find lots of anti-union organizations because corporate owners are happy to fund them. They talk a lot about mafia involvement in unions, so evidently the corporate-funded anti-union organizations think it helps reduce political support for unions.
Although the mafia may have helped destroy the union movement in the US, other forces are much more important for explaining both the dramatic rise unions and their fall. Unionization had already began to fall when the FBI finally began cracking down on labor racketeering (as mafia involvement is called) in the 1970s. The mafia’s involvement in unions was mostly destroyed by the end of the 1990s or shortly thereafter (according to one researcher and the FBI) but unionization has continued to decline since then. Plus, there were unions without organized crime such as the Congress of Industrial Organizations (CIO) that were not infiltrated by the mob whose fortunes mirrored with the rest. Today, the three biggest unions in America are unions that never had mafia ties: the National Education Association of the United States (teachers), Service Employees International Union (health and gov’t), and the American Federation of State, County, and Municipal Employees.
As this list shows, the only unions that have continued to thrive in the past half century are the unions whose employees are mainly funded by government: teachers, health workers, police, firefighters, and other government employees. These are also the only unions that have never been opposed by a concentrated interest group (corporate owners).