"If they mean Muslim - why not just say Muslim?"
Asian is an ethnic description, not a synonym for Muslim. I believe Americans may use 'asian' when describing someone of Chinese origin, for example. Why does it bother you so much that, in British usage (for obvious historical reasons) it tends to be used for people of Indian, Pakistani or Bangladeshi descent?
Becasue the term "Asian" means anyone from Asia - hundreds of different cultures. Why do Brits narrow it down to just three? Especially when actually referring to Muslims? Most Asians are Hindus or Buddhists - NOT Muslims, so why use the word "Asian" when you are only referring to Pakistanis or Indians?
That's like referring to Brits, Greeks, Russians, Swedes, Irish, Germans, Italians, Hungarians and Serbians all as "Europeans".
While it is true that a Swede is a European - it is NOT true that a European is just a Swede.
Same thing with "Asian" and "Muslim".