Is a cat allowed in an uber if hes in a cat carrier?

Yes, as long as your driver is cool with it. Just give them a quick call after you have requested your ride to give them the heads up. Most will say yes but you will run across people who say no or are allergic to cats.

The rule is that there isn’t a rule. It’s basically up to the drivers. 

A cat in a carrier should totally be okay, unless the driver is worried about allergens. (Some inevitably are sensitive.)

It should be 99% okay, but if you want to be doubly sure, text the driver upon being accepted and ask if it’s okay.  The likely answer is yes, and he or she will appreciate you asking. (The 1%, the driver will cancel but you can just call another one.)

Yeah shouldn't be a problem.

I'd give you a ride, better than a shedding dog that wouldn't sit down in my back seat.