I can understand why Gates thought and felt the way he did. Gates is 75yrs and who has most likely experience a lot of racism during his early life and that affects a person perception on how they view situations especially if you have been in a similar situation before as a young man who felt he had no voice. When being confronted in your own home and "not knowing why they are there, regardless of what the officer stated" I can see being extremely pissed off to prove it's your residence as a "black man" living in a nice area.
"Man/Men" is the key word in this situation not racism.
I understand Crowley was doing his job. He was taking verbal attacks from Gates while performing his job, which would also piss you off whether you are on or off duty. But being on duty you should take the higher ground and not be reactive and take it personally.
What it boiled down to was who is the bigger man I believe Crowley was pissed along with Gates, but wanted to prove who had the power since his pride had been affected. It was two men trying to claim there territory. I believe Crowley wanted to show him who had the power due to their interaction not his race.