This is a common, and very legitimate question.
For openers, here's a link to one of my posts on the Everything Uber/Lyft thread that talks about the stringent
background checks all Uber drivers have to pass:
Everthing you wanted to know about Uber/Lyft at WDW
Lyft has similar requirements, at least in Florida, because our state law requires that level of background investigation for all rideshare drivers.
Taxi drivers are regulated locally, usually by the counties. I don't know what the Orlando area requirements are, but there are background checks of some sort, and they are probably along the lines of the Uber/Lyft checks.
Just in the last couple of weeks, Uber has now adopted a policy of re-checking driver backgrounds at least once a year.
Driver and car identification
In addition to the drivers' background checks, there are several other protections. With both Uber and Lyft, when you order a ride, you will be given the driver's real first name, a description and tag number of their car, and a photo of the driver's face. Always check the face behind the wheel against the driver picture on your app. That's the best safety check you have.
Uber periodically requires us to do an immediate on-app facial recognition confirmation -- to ensure that the person using the driver app is actually their approved driver. Lyft does not do this; my Lyft pic is the original.
Ride tracking
When you are in an Uber or Lyft ride, your ride is being GPS-tracked in at least two ways. You are being tracked on both the driver's app and your rider app, through the ride and for a couple of minutes afterward in the case of riders. So Big Brother is watching over you throughout your ride. Obviously, the driver is tracked constantly.
With Uber, you also have the option of "sharing your trip" with trusted family or friends. You can set up people to share, and they also will be able to track your ride in real time. Lyft may have a similar feature; I'm not sure.
Uber is also rolling out a safety update to the rider app that will apparently feature a suite of new safety features, including a button to automatically dial 9-1-1 directly from the rider app. I haven't seen that update, so I'm not sure what else is in it.
So as you can see, the safety features in rideshare are quite robust. No system is perfect of course, but Uber gives millions of rides every day worldwide with a very very low incidence of problems.
Bad news is always a click-magnet for news media sites, so bad news gets prominent attention. If the news media thinks a criminal has ever driven for Uber, the word Uber will be in the headline somewhere...whether the issue occurred on an Uber ride or not. Real problems are very rare, but they do occur -- with Uber drivers, doctors, lawyers, clergy, police officers...every group. Pobody's Nerfect.