LOLOLOL!
Yeah, only if you want a JOB in certain parts of the US.
There are absolutely places where union membership is mandatory in certain fields, otherwise, you're unemployed.
Only in states with right to work laws. In other states like New York, not so much.
You are technically correct that in some states you do not have to be a union member to hold a union job. However, you still have to pay to union dues regardless of whether or not you choose to be a member of the union.
How do you figure? In many union shops in non-right-to-work states you will be fired if you do not join the union within a month or so of employment. Do you mean that it is not mandatory in the sense that one doesn't have to choose to be in a union?
And if you are a Beck objector, you get no union benefits like representation in disputes or the right to vote on contracts.
See: http://atyourservice.ucop.edu/employees/policies_employee_labor_relations/agency_fee/bill_sb645.html
As of January 1, 2000, all employees of the California State University or University of California “as a condition of continued employment” had to either join the union or pay a ‘fair share’ fee to the union (which was if I recall correctly about 95% of the union dues). It is the law in the state of California. The practice continues to this day.