Yes some people can be intolerant to coffee just like you can be intolerant to many other drinks, food etc.
Some people are naturally intolerant to coffee and have a coffee intolerance.
Symptoms of a coffee intolerance are things such as involuntary muscle spasms, elevated heartbeat or blood pressure, stomach cramps, upset stomach, anxiety, Insomnia or trouble sleeping and irritability as well as feelings of jitteriness and unease.
If you experience any of those symptoms after drinking coffee then you could have a coffee intolerance.
If you're intolerant to coffee then it would be best to stop drinking coffee and speak with your doctor.
You might be able to drink decaf coffee when you have a coffee intolerance but sometimes you still might be allergic to the coffee and not be able to drink it.