I'm pretty sure I'm not an empath (I can be pretty thick when it comes to realize other people feelings sometimes) but i have experienced the accent appropriation many times before. During Summer I spend 2 weeks in a sort of outdoor camp, with people coming from all over the country. There is a very distinct difference between south and north accents. By the end of the 2 weeks, most southerners are using northern accents and viceversa and no one realizes it until they go back to their own cities and see how differently they are talking than those around them :P

So I'm guessing that as an empath you might get this happening much faster which can be annoying, but dont worry, you are not alone. Every time i go back to my city after the camp, my friends and family all mock me saying things like "Oh, look who's turned southerner in 2 weeks! Can't imagine what would be like in a month!"

If someone gets offended, well, its their prerrogative, but just try to explain you didnt do it consciously.