There is no federal law that prohibits financial sector employees from unionizing. In fact, the National Labor Relations Act protects employees who seek to unionize and collectively bargain with their employer. The Act applies to Wells Fargo and you'll see statements and procedures littered throughout the Handbook and other personnel policies designed to ensure compliance.
All that said, unionizing has become more and more difficult over the years. The federal government's position has become much less friendly to unions and much more pro-business. I remember reading stories about the Committee for Better Banks and Wells Fargo at one point, but not much recently.
Unionizing is not an all or nothing proposition. Different employee groups with different functions can unionizing while others do not. The NLRA outlines all of that stuff, and a lot of information about the process can be found on the National Labor Relations Board's website: https://www.nlrb.gov/