Even if they were invited, they would have been required to sit separately as men and women do not sit together and do not mingle.
It is one thing to do this at a Muslim meeting, but when he carries on those practices on a normal basis, this would be at least an indication that he is a Muslim or favors Islamic practices.
Remember how much cajoling it took, to get him to wear the American flag lapel pin.
If someone were to list all the indications by mannerisms and action, incidental and overt, that Obama is a Muslim, the list would be in the hundreds.
****females have no standing or rights in Islam****
he does, however, have a great number of female appointees in high positions.