Yeah, I do. Characters like Peter Parker were conceived and written as he was, as soon as you change something he suddenly becomes a completely difference character.
I don't mind adding depth to a character, adding elements that may have not been established when the character was first invented. But when you change something fundamental to a character such as race, gender, or upbringing you essentially make a whole new character. At which point you're no longer writing Spiderman, you're writing about a whole new character with spider powers using the Spiderman name for recognition.
If the change is fundamental, but also doesn't add anything to the character, then the change itself is completely pointless. In the point of Spiderman, I understand there should be no discrimination towards the actors; but imagine if this was done for the comic series? It'd be weird and out of place, much more then the movie would. Though on the other hand, I wouldn't mind seeing it. You can take a lot more chances when it comes to comic books.
All in all I don't like it, unless the series is meant to be a "What If" Scenario. If it was "What If" it'd be an interesting take on it. If it's a reboot and you make an established character a difference race "just because" then I don't like it.