I'm trying to figure out through the interface as well as via the documentation and blog articles if Azure has a PaaS option that runs on top of Linux instead of Windows.
Azure now offers App Service (which hosts Web Apps) on Linux. Currently it's considered Preview and only available in a few regions, but... it's announced and available.
More information may be found here.
Presently, the answer from Microsoft/Azure is "not in the short term, but it could happen later".
As we are talking about PaaS, optimistically speaking and by design, the platform shouldn't be a consideration. For many situations, this should be true, although there may be exceptions when functionality does split along OS lines. The best example would be a native library integration on your platform of choice - of course this cuts both ways as there may be some libraries only available running on Windows as well.
The only remaining difference would be performance, but if that's an issue, then it stands to reason it should be raised as a support item.
The takeaway here is that there is a very strong case for selection so that people can choose the operating system that best suits their needs.
I've created the corresponding feature request which you should upvote if you're interested in seeing this happen.
If you're interested in advocating a bit further, you can also consider retweeting this to your friends and colleagues.