"But can this type of speaker system cause these problems???"
Assuming the phone works OK with the sender switched off, the answer has got to be yes.
Phone receivers are designed to pick up very small signals in the order of a few millionths of a volt. The physical size of phones limits the tuned circuits that can be employed. Close proximity to a transmitter on a different frequency is likely to de-sensitise the phone receiver and give the problems you're encountering