Even 'reasons' that violate our constitutional rights? I know that several State legislatures & at least the Georgia Supreme court disagree. They say that your car is personal property, and it's legal contents cannot be used as an excuse to deny you employment.
Illegal searches are being misused by companies in order to fire otherwise law abiding employees. -- Employees who are exercising their RKBA's in their cars.
The employer has no right to coerce you to either own/carry or avoid owning/carryihg a gun.
There is no question, or dispute on that point.
But he does have the right to avoid hiring you, or to fire you. Why? Because of his property rights in his capital.
His property rights do not trump your right to have a gun in your car. Firing you for that 'reason' is constitutionally 'unreasonable'. As you say "everyone has the same rights equally."
And any suit against an employer based on the idea that an employee was improperly fired due to gun ownership should fail for the same reason that a suit against a private individual that claims damages for refusing to buy product from a particular vendor (for whatever reason) should fail. You have the right to decide whether or not to buy something, and from whom. An employer has exactly the same right--because everyone has the same rights equally.
Any suit against an employer based on the fact that an employee was improperly fired due to gun ownership should win, -- based on the idea that employers have no reasonable basis to infringe on our rights to have arms in our cars.
Why would you approve of employers property rights trumping employees gun rights?
Corporations (in their many and varied entities) are creations of Government; they do not have Rights -- they are granted Powers from their creator governments. Powers can impede or restrict Rights under limited and specified circumstance, but cannot abrogate those Rights.
You have a Right to fly anywhere in this country -- if you wish to do so on a commercial airline you are subject to search at any point during that trip. Should you wish to not be subject to those Powers of search, then you are free to fly yourself or hire a private plane.
While similar in application and intent, Powers and Rights are not the same; they are neither exclusive or inclusive with respect to each other.