When it comes to integration, there's certain things Muslims will not do. We won't drink and we might dress differently.
These things do not mean we don't integrate. We go to schools, universities, we work, we put into the system etc. We contribute more or less the same as your average person.
The racists will never be happy with our efforts.
Put it this way, my husband's grandparents lived in a small village and his grandma went to the church when she could. Other than that, they were absolutely not integrated into the community, they kept themselves to them themselves.
No one would say they weren't integrated.
My mother is part of her community - she attends the mosque and organises events for the local community there and she's well known locally with plenty of friends, but she'd 100% get accused of not integrating as her immediate community is mostly Asian/muslim because of where she lives.
Who is actually integrated in all parts of society? We all live pretty siloed lives in the UK yet the burden to prove themselves integrated is always on the 'foreign' looking ones