Guys you people are taking it in religious sense.
Let me re-phrase the question (forget about the term muslim athiest)
Are there people who do not beleive in God but consider teachings of Islam as best way of living?
Peace Iconoclast
I think 'no' it is impossible to have that. The reason I give is because of belief. There are apparent benefits in the Islamic way of life, but there are hidden ones and there are things that are 'true' but not obvious.
If a woman was earning $1500 per month and her hubby $3000 per month, their rent comes to $1500 per month.
One person says it is fair to give 50:50 towards the rent, another says no, she should give the same in proportion to what her hubby is giving. i.e. she gives $500 and hubby $1000 per month so their proportions are the same ... rent:salary.
However, Islam says 100% given by man, regardless of woman's income, unless she wants to give to make things easier, but then she gets two rewards. One for giving two for under no obligation.
The last option will never come from a man who does not believe in God and if Islam says this he will see it as illogical.