Indiana is an "at will" employment state. Employers may terminate you at their discretion for no reason what-so-ever. So unless you can prove that you were terminated wrongfully as a result of discrimination then... well you're pretty much out of luck.
Tn is the same. Unless there's something in a company handbook or other written policy that states reasons for termination, employers can terminate at will.
Tn legislature is taking up an issue over "employees guns in car" right now. A year or two ago the state law was changed to allow employees with carry permits to have guns in cars. The law doesn't have any teeth because Tn is a "fire at will state," subject to the above exception. To my knowledge no one has been fired for having a gun in a car but gun rights advocates have been trying to get the law changed.
I don't know about employers rights to search vehicles. I'm pretty sure they would be able to do so if a condition of employment involved forfeiture of the right against such a search. Employers may be able to search at will but I don't know about that.
As to the comparison of an employer's policy against carrying to that of discrimination based on race, there's a difference. I'm not a legal expert but there are differences between a Constitutional Right and a Civil Right. In this case, the right to own and bear arms is a Con. Right, but not a Civil Right. The right to not be racial discriminated against in employment is a Civil Right.
The civil right is between a protected group (based on race, sex, religion) and an employer. The Con. Right is between govt and individual (sometimes between Fed. govt and state gov. depending on the right). An employer can have a rule forbidding the carrying of a firearm at work, but could not have a rule forbidding blacks, Baptists, or women from carrying but allowing white men to carry. I may be wrong about this distinction but I think its generally correct.