Does rooting an Android tablet make it easier to keep secure than leaving it unrooted?
Rooting process of Android device does not make it vulnerable in technically point of view, you're removing one layer of protection and expecting the other security measures to compensate, but in practice you would be installing applications with root privileges which may execute malicious code. On Android device configuration, no applications can access any other applications data, no matter how many permissions the application asks for. When you run an application as root, this application is no longer running in a security area because it has access to the entire Android system. An application with root permissions can read other applications data as for example the way Titanium Backup works and why it requires root. If you know what you’re doing, you should be okay with your rooted Android Device, but you’ll need to be more careful.
With Rooting you can reduce bloatware and factory installed adware. This technically does improve security and can be considered useful for removing services.
Some malwares can gain root permissions even on a un-rooted phone
Android Security Overview
Also, rooting gives the user access to some options/permissions that are locked away in stock Android, so if someone roots their phone and doesn't know what they're doing, they could create problems. So if security is your main concern, rooting is probably not the best option for you.
Rooting an Android device actually lowers the security of the system. This is because it allows the user and applications access to the main system files, in turn making it possible to make serious changes and/or damages to the system. The only way rooting can help security is by being able to install the latest compatible firmware onto the device.