In and of itself, it is not offensive - Muslims don't have a monopoly on head-covering.
If someone is specifically wearing a style of head-covering that specifically seems to identify them as a Muslim:
* Clothing is a form of social signalling and identification. It is worth mentioning that, in general, the hijab comes with a package of values, beliefs, and social expectations (for instance, it is generally assumed that women who wear hijab pray regularly, are committed Muslims, behave in accordance with certain Islamic norms, do not date before marriage, etc), just as one might expect someone wearing a priest's collar to behave or not-behave in certain ways. So it is worth taking that into consideration. At the very least, someone might be surprised if they see a woman wearing a hijab buying bacon, for example.
* If someone is doing it to fetishize Islam and as a popularity stunt, it could be offensive and a form of cultural appropriation. For instance, if someone wears a a Muslim-style headscarf but posts sexually explicit photos, a bikini photo, a bar photo, etc. Some magazines and media outlets these days have caught on to the idea that "Muslim-ness" can be a great selling tool and some of the ways they use this to sell fashion is offensive, or, at least, against the spirit of hijab.
So, basically, if someone is choosing to wear a headscarf style that specifically makes them look like a Muslim, it would largely come down to intent and how they are presenting themselves and if they are doing it respectfully.
Also note that people vary in their views of what they personally consider offensive or not. Some Muslim women might be very happy to see other women wearing the hijab and others might be taken aback. It's difficult to please all the people all the time! In my view, the most important thing is just to be authentic to yourself, whatever that might mean for you.