iPhones, iPads, and Macs share a messaging platform they call "iMessage". These iMessages appear blue on your device and use internet to go around. So if your parents use the same Apple ID as you do on their Apple Devices, then yes, they can enable a feature to see your messages.
However, messages sent through usual Text Messaging (they appear green) generally are received only by an intended person.
One must be very well versed in hacking to hijack a text message. (I'm not even sure this is possible)
I hope this helps,