Six current Boston Red Sox were, at one point in their career, part of the New York Yankees organization. In the not-too-distant past, it would have been criminal for this many players (23% of the roster) to have been from New York, especially when three of them came directly from the Bronx without a stop in between.
Recent times have seen the two teams make a couple of trades, although nothing groundbreaking, showing the softening borders between the two. That doesn't mean that Boston using their former players against them won't make a potential series victory over them that much sweeter for Red Sox Nation.