Allah orders women to wear hijab or niqab in the Quraan.
Openly live and practice? No. Actions have implications on societies as whole. Acting on emotions towards the same sex is considered a major sin and we dont want our children to grow asking why two men are living together.
Based on these two answers alone, I know I am not interested in living in even your "ideal" Muslim society. Sexually repressed cultures that discriminate against women, sexual and gender minorities are quite disgusting places.
As for those who leave Islam, I leave this for scholars to have the say about it.
And what do they say?