What would cause a broadcast AM or FM radio to receive an amateur radio transmission unintentionally?
Why This is a receiver problem, not a transmitter problem. Consumer broadcast radios are built cheaply, with little front-end filtering, so a strong nearby signal on a completely different frequency can get into the first stages, overload them, and be detected as audio. The cure is at the affected receiver: better filtering, a bandpass or high-pass filter on its antenna lead, or more distance, since your transmitter may be perfectly clean and legal.
Watch out Excessive mic gain, an overdriven audio stage or wrong FM deviation are transmitter adjustment faults that cause distorted or splattered audio on the amateur signal, not the reason a broadcast set hears you at all.
Cheap radio, poor filter: fundamental overload is the listener's receiver failing to reject your strong out-of-band signal.