No.

You can lie about union organizing because an employer is not allowed to use whether or not you are a union organizer when making hiring or firing decisions.

If you lie about something that the employer is allowed to use in making those decisions they can fire you.

> So, all you have to do to completely lie on your resume and keep employed, is pretend to be union organizing?

You can lie about your union involvement. You can't make up qualifications you don't have.

Inventing qualifications is probably still not legal.

Now, not mentioning a job in the past, or some details of it, are a different case.

I'd imagine it'd go to court and the union would have to testify that this is the case, and also have documentary evidence to back it up.