When all the employees are required to be union members, there are usually rules imposed by the union affecting the "at will" nature of the employment. They're not strictly linked, but the one affects the other to some extent or another.
'At will' is the operative thing here, not 'right to work.'
'Right to work' laws make it illegal require union membership.
Unless you have an employment contract you are most likely an 'at will' employee and can be fired at any time the employer wants you gone.
They are VERY different and separate issues.