Interfering with a union or the formation of a union are explicitly illegal. This includes firing someone for trying to organize, at-will employment or no. However, this doesn't keep employers from trying, or from retaliation using pretextual explanations to avoid penalties. It's also common for employers to force employees to watch anti-union propaganda. Much of the overall culture in the US, as well, has turned hostile to unions.
State and federal law have been growing increasingly hostile to unions. Since 1910, if a union is formed by way of a majority vote of the employees, then they are required to represent all employees, whether or not they pay dues. Many states, including New York, California, and most "blue" states, allow "union shops", requiring all employees to pay dues whether or not they choose to join. But many, including most "red" states, have "Right to Work" laws banning union shops and allowing only "open shops". Any employee can therefore benefit from a union without contributing to it. The immediate free-rider problem cripples labor organization in those states. The problem is compounded by manufacturers moving their production to RtW states to save on labor costs. Boeing, for example, has moved much of its production from Washington, where its employees are unionized, to South Carolina, where they aren't. Membership has fallen from 20% in 1984 to 10% in 2018. Moreover, the Supreme Court ruled in 2018 that unionized public sector jobs must all be open shops, overturning a 1977 decision. That covers about half of the country's membership, so we can expect it to weaken labor even more in the years to come.
The overall result is that the power of organized labor is a pale shadow of what it was in the mid-20th century.