I think a white Jewish or Muslim person who doesn’t wear religious dress shouldn’t be classed as BAME. Those who do wear religious dress would be a white minority ethnic group - in the same way some travellors are.
Lol.
White Muslim converts are not at all an ethnic group because they only have a recent philosophical view.
White secular Jews may be an ethnic group since they have shared culture, names and other markers which identify them as Jewish, even if they don't believe.
For example someone called 'Goldsmith' is going to attract foaming hatred from far left and far right simply because of their name. The far right will look for white people expressing pro-LGBT or other views and seek to identify them as Jewish as distinct from white.
The far left will look at people with Jewish names in politics and finance and blame them for everything.
They are clearly identifiable as an ethnicity because they are noted in media as Jews, have names, may look slightly different from white people in various characteristics. French people are also an ethnicity and can be identified similarly but for UK statistical purposes are grouped as white Other, along with Jews (who may also identify as white British)
Travellers are specifically separately identified as an ethnicity in UK statistical terms. Jews are not.