Complete and utter nonsense. Admittedly the drug policy is strict here although you'll find a lot of people who smoke weed. Alcohol is openly available in hotels, clubs, and your own home.
Dubai is more tolerant of women than most other places in the world, to be honest. There are still some inconsistencies in immigration law but that's about it. If you're a Muslim, things become much stricter but I can't speak for that personally.
They've done away with the restrictions on unmarried couples living together and every month they're announcing new initiatives bringing the UAE in line with the west.
99% of things operate on the policy of you can do whatever you want within the confines of your own home but if you start causing issues in public, they'll come down on you hard.
We are across in 3 weeks time for 3 weeks and this will be our 20 something visit in 12 years. We've found it's a totally safe place and great for winter sun and a great stop off on route to Singapore or Thailand.