I have an LG Rebel 4 and its been having problems so I feel I should factory reset it, but im concerned that it may effect the accounts (which are the exact same as on my phone) on my Tablet, as I really dont wanna lose them.
A factory reset just deletes all your user data locally on your phone. Data stored in the cloud and synchronized to other devices linked via an account and are not affected.
Even if you don't trust these information you can make sure no remote account is affected:
Before performing the factory reset from within Android settings activate the Air-plane mode. Now there is no chance that any account can communicate with a cloud server to tell the server that you are resetting your device.
And after the factory reset all user data has been deleted therefore all information about accounts and other saved data is gone, hence after the factory reset when you re-establish connection to the Internet there is no information available what accounts were present before you performed the factory reset. SO the device can tell nobody that you performed a factory reset.
From the perspective of the cloud services/accounts your device simply went offline and did not came back online.