Having high neutrophils counts can be dangerous and mean you have an infection or even sometimes cancer.
However not everyone who has high neutrophils when tested will have cancer or other infections but if you do get tested and have high neutrophils then the doctor will usually want to do some other tests.
I've had high neutrophils before and it turned out that I didn't have any infection or cancer which I'm thankful for.
However there have been some people who have had high neutrophils and then had either an infection or cancer.
But the high neutrophils itself does not always mean or indicate you have cancer or infections.
So it's best to not worry until you get the full tests done.