It's too old-fashioned to be offensive. Someone might use it in a jokey way.

The only people who ever really used it were the Yanks and Irish. But nothing like that is offensive among native speakers unless a person is stupidly sensitive. Yanks, Brits, Jocks (Scots), Taffs (Welsh), Paddies (Irish), Canooks (Canadians), Poms (for Brits in Australia) are all acceptable in the right context, by which I mean an obviously friendly context. For example, you're on a 3-day sales course and there's a Welshman among the delegates: native Brits will automatically call him 'Taff' and that will be his nickname unless he really objects (which he won't).