same meaning?

Let’s say John has offended me recently.

Do these sentences have the same meaning?

[i]John is the first one to offend me.

John is the first one who offended me.[/i]

I think more information is needed to decide if either sentence is suitable.

Does “first one” mean the first person to ever offend you in your life (seems unlikely)? Or “first one” in some particular situation where other people later offended you? If the latter, you would say “John was the first one to offend me”.

What you suggested “John was the first one to offend me” is in the past tense.

When do we use the present tense i.e. is the first one to offend me"?

“John is the first one to offend me” is relatively unusual. It could be part of a narrative in the historical present tense; it could be describing habitual action (“every time I go and visit the family, John is the first one to offend me”); it could be describing an offence that happened in the past but where the novelty of “first one” still feels very current (“People have been calling me all day, but John is the first one to offend me”). There may be some other cases that don’t immediately come to mind, but, as I say, you will probably rarely need to use the present tense here…

How about live sports commentaries or newspaper headlines? E.g. …and John is the first one to score! The present tense is possible here, right?

Yes.