No, the constitution protects you from the government searching you and so on against your will. My dad's factory is not a government agency, and you provide your urine of your own free will. He can't make you. You have a choice!!!!! He just won't hire you. No law against that. As an employee, think of yourself as a tool for the company so to speak. You want the best tools possible. You wouldn't do precision machining with a Harbor Freight lathe? You get the idea.
His company also makes his guys and girls cut their hair, or else it has to be compressed under a helmet. If it doesn't fit, then you get it removed. Lots of heavy machinery and rotating machinery, its not a safe place for loose clothing/hair.
Guess what, I have to wear a uniform to work, shave, have my haircut a specific way and so on. I can't bring my phone to work, and I get random searched all the time, for no reason, just cause, just in case I might have a phone. Where is the ACLU!!! My rights are being violated!!!
No, an employer should be able to do an initial drug test, he is investing time in money on you. He should be able to tests if there is an accident, or reasonable cause. If you don't like it, work somewhere else. Thats the glory, you have a choice!!!
I would test drive a car, check the oil, and so on If I was buying a home, I would have it inspected, check the attic and so on. An employee is potentially a 50 year investment.
Here is another good one, if I get in trouble out in town, say a DUI, I do my civil court stuff and so on. Then I come back to work and do it again, where I get reduced in rank,(lowered pay, no chance for promotion...and possibly even fired. You would expect that since your tax dollars are going to fund this operation, you should have safe operators. Essentially I work for you. Wouldn't trust a drunk/drug guy with a million dollar machine would you? Would you want to put your life in the hands of a heroin addict? Working in a factory with 200 ton presses, metal saws, robotic welders and so on is no different. Its a dangerous job if you aren't paying attention.
I am a volunteer in the military, I knew the rules when I signed up. I had a choice to not work here.