Communications system providing text-to-speech message conversion features using audio filter parameters and related methods

A communications system may include at least one mobile wireless communications device, and a wireless communications network for sending text messages thereto. More particularly, the at least one mobile wireless communications device may include a wireless transceiver and a controller cooperating therewith for receiving text messages. The controller may be switchable between a normal message mode and an audio message mode. Also, the at least one mobile wireless communications device may further include a user interface device connected to the controller for receiving at least one audio mode filter parameter from a user, and an audio output connected to the controller. The controller, when in the audio message mode, may select received text messages based upon the at least one audio mode filter parameter, and output audio messages including speech generated from the selected text messages via the audio output.