I'm not good in English or Latin language, but as far as I know 'cult' is from Latin 'cultus' which among other things may have something to do with worshiping. Maybe in English it has negative connotations but for example in my native language it does not matter if you say 'cult of sun' or 'cult of Jesus'.
Yes, cult means a system of worship and is an appropriate term to use here. It is commonly used like this in historical and archeological discussions. In recent decades, the most common use in popular culture has been as a label for some very unusual or even violent religious groups. Based on some posts here, even some religious studies programs are avoiding using the work for fear of this popular view of the word.
