Most of my local friends drink, both men and women.. Last week I went to the Wehm lounge at the W with friends and I noticed a sign board outside saying Qatari women are not allowed.. Which means clearly that Qatari men without the their white garb can go in.. As far as the women are concerned, they usually book a room in the hotel then go to the bar and give their room numbers instead of the ID cards and they are let in because hotel guests do not require to present an ID card. If they do not want to do that, they can just go to a five start restaurant which has a bar as well.. For instance the Spice Market or the Market, both restaurants are at the W and they do not ask for ID cards so anyone can go and eat as well as drink.. They have happy hour everyday from 5 to 7 so it does not matter what is your nationality or your dress code, you can go in and drink to your hearts content. Besides that, you can also get in the bar at Kempinsky hotel ground floor without an ID card as long as you get in before 5.. On Fridays they provide free bubbly to all the ladies. Trader Vics at the Hilton also does not ask for an ID so nationality is not an issue.. Most restaurants which serve liqor as well do not ask for ID cards..
Secondly there are no such things as alcohol laws, except that you should not drink and drive or hit on women when drunk, actually do not hit them at all,period.. QDC gives out liqor permits to just anyone who has a reasonably good job and a decent pay slip. They don't ask for religion and in any case most passports in the world do not mention your relgion and even the Qatar ID does not mention religion so how would they know if you are a Muslim or not..