Is it legal for an employer to make a policy that only affects on person within that company?

I guess I can be specific. I work at a car wash. One of my responsibilities is to replace the chemical barrels in the chemical room when they get low. These are the chemicals that are dispensed on the vehicles when they go through the wash. The vast majority of the time, I'm the only one who deals with these chemicals.In October of last year, I was changing out a chemical barrel, I accidently over filled it with the remains of the previous barrel and I quickly took the funnel out and put it back into the bucket that had the last little bit of chemicals from the previous barrel. When I did this, the chemicals splashed up into my eyes and I had to go to the medical clinic to have them flushed out with saline solution. Ever since then, when ever I change out the chemicals, the "powers that be" made me where safety glasses when changing out the barrels. Today, however, there was a clogged tip on one of the lines where the individual chemicals go into the dispenser. I tried to unclog it, but it wouldn't unclog. This is something that I've done many, many times without safety glasses because this task doesn't require them to be on in order to be done. Well, the general manager saw me doing this and freaked out and said that I'm banned from the chemical room because I "burned my eyes." Well, this irked me quite a bit because it feels that I'm being targeted. What I mean is -- there's being safe and there's being paranoia.