How can you address the potential problem of Muslim out breeding EU and UK without sounding like a racist BNP?

Easy, leave race/ethnicity/religous affiliation out of the discussion. Your statement confounds the "potential problem" with "Muslim out breeding." Presumably, this is not a problem in and of itself, but may have some other deleterious effect. If race/ethnicity/religious affiliation itself is the issue, then I would say that it probably sounds racist because it is racist.