I agree it sounds better without the "and", but is nor actually wrong.
If you are going to say "precautions" I think you really need to say what kind of precautions. As well as "safety" precautions, you could take "security" precautions to stop your T-shirt being stolen, "laundry" precautions to stop your T-shirt shrinking etc. Taking "fashion" precautions probably rules out wearing the T-shirt
!
You could say "...safety precautions and security precautions", or just "...safety and security precautions", so "...safety and precautions" sounds like there is word missing. But I don't think it is actually wrong, it just sounds a bit odd.
Also, the phrase "safety precautions" is so commonly used that any variation sounds odd anyway.
I think I need a "taking all unnecessary grammar precautions" T-shirt!