Anyone that finds the British to be racist probably hasn't spent enough time in rural Texas or Alabama.
Perhaps the British were that racist hundreds of years ago, but I don't think they are any more.
I mean, if the British were racist, then they would probably treat White Americans better than, say, a person of a different race that was born and raised in Britain. Do you really mean to claim that they would? I mean, sure, maybe they'd like the fact that I speak English as a native language and that they can pronounce "Jeremy Andrews" more easily than "Jose Gonzales" or something. But that has little to do with my being White.
I think what a lot of people from wildly differing cultures don't grasp about Western society is that it's just not that tribal. Everything is about laws, politics, interest groups, national borders, and individuality. People of the same culture, race, and language often go to war over ideals and sovereignty. People don't flock together or help each other on the basis of skin colour. They form unions, perhaps join churches, clubs, or political parties, but they don't go around thinking, "I've got to go help out White people because I'm White". That's rarely even a major aspect of their identity. I see it occasionally among people from other cultures that have more in common with each other, but even they end up excluding their own people that choose adopt the local culture as "traitors" of some sort. It's more common for race to be used as a misguided, superficial indicator of culture, than for people to genuinely believe in race as a valid construct.
I would guess that they prefer people who adopt the British culture regardless of race. Being ethnocentric or having a negative attitude towards a certain religion is not the same thing as being racist, although it can look like that to recent immigrants of a different race who live according to different cultural values. I'm pretty sure most of the people complaining about Islam are not racist. If they had to choose between a White person that spoke Arabic and worshipped Allah, and a person of Arab descent that was a tea-drinking, cricket-playing Protestant with a British accent, I think anyone could easily predict that they would prefer the second person to the first one.
Now, is it wrong to be ethnocentric or dislike certain religions? You can make a very strong argument that it is, but that argument is separate from the charge of racism. You can't generalize all forms of discrimination against an out-group as "racism", because that's not what racism means. Racism means you are being discriminated against because of immutable and heritable aspects of your appearance, like skin tone, face shape, or bone structure.