The employer must only have "reasonable suspicion" to terminate an employee for violating company policy, i.e., no firearms or other dangerous weapons, on company property, to include vehicles, not probable cause, preponderance of evidence, or guilt beyond a reasonable doubt. The employee normally has to acknowledge that they have read and understand the rules of the employer, which may include written consent to search as a condition of employment.
As the person who had to draft this type of policy for an organization, it is not easy to limit what I consider an abuse of constitutional rights, however, every employee is informed of their obligation to follow company policy, IF they want to stay employed.
The firearms prohibition that I wrote was in the organizations's workplace violence policy. Our intent was not to limit the individual's right to own a firearm, but to restrict firearms in the workplace. This may sound a bit alturistic from a retired LEO, but like every other employee, I knew the limits of what the leadership would accept. With a significant workplace violence episode in the state that made national news (Lockheed-Martin plant in Meridian), there was pressure, primarily from the insurance carrier, to insure there was a policy in-place to prohibit such activity, i.e., limit liability.
If an anonymous call is received that an employee has a firearm in their vehicle, and there are no other indicators of violent or erratic behavior, a single report may not rise to the level of reasonable suspicision. However, if the employee is asked if they have a firearm, and admit they do, it's an automatic termination. Likewise, if they deny it, and later it is determined that they lied, it's an automatic termination.
Like others have said, if you can't abide by these rules, then you should find somewhere else to work.