Generally speaking, racism and bigotry become less prevalent as education standards improve. As a very technical Service, the RAF needs a very high proportion of intelligent and highly skilled personnel. In my experience, the RAF is very partial to your conduct and competence - but does not give a damn where you are from, what accent you have or what colour you are. Having a Daddy who also served in the 'King's Own Royal Donkey Wallopers' will not help you - your brain and ability to work in a team will.
I am not saying that is does not exist but it certainly is not tolerated. I don't think he would mind if I posted that the Jag force have a flight commander with first-generation Indian heritage (poor chap does have to endure appearing in an inordinate amout of
PR shots though!) so you need not be concerned as to any race-ceiling.
As I recall, the BBC did a 'Look East' series, one programme of which focused upon Asians in the Armed Forces, almost all of whom were very positive. You may be able to track down a copy - it would give you a useful second opinion.
Bottom line is come on in - if you are good enough, you'll do well!