I don't want it to look like I'm defending Google, but being based in KSA, I can provide some info on the app. Absher essentially facilitates services that can be availed of on the site www.moi.gov.sa --- relative to your Residence permit, ID, visa, passport, license, etc. I've used it primarily to retrieve info and ensure my details are valid --- which is of importance since I'm an expat.
(For example, should the sponsoring company inform me that they've renewed my residence permit, I won't just take their word for it but will verify it, either on the website or using the app.)
As for it violating women's rights, the fact is there aren't many of those here in the 1st place. If you look at the legal system here you'll see that women tend to be treated as minors & are under 'guardianship' of their male relatives, so even if the app isn't allowed on Google Play Store & Apple Store, it isn't gong to make much of a difference since the website can still be used.
Remotely related to this: Most countries require that non-citizens obtain a visa to enter --- KSA takes it further by mandating that you get a visa to leave. This has to be approved either by a sponsor or --- in the case of a lady --- by a husband / father. I was whining about this to someone in HR, and he was like: Look on the bright side --- if you get your wife here, she'll never be able to leave you... 
Look on the bright side --- if you get your wife here, she'll never be able to leave you...
Nope, sorry, I don't find it funny ...
