Neutral:
* Meantled
* Intervened
* Meddled
* Impinged
* Involved
* Bothered
Negative:
* Impeded
* Obstructed
* Hindered
* Disrupted
* Tampered
* Intruded
* Trespassed
* Butted in
* Sticked their nose in
* Got in the way
* Crossed the line
Positive:
* Assisted (if the interference was helpful)
* Helped (if the interference was beneficial)
* Interceded (if the interference was to help someone else)
The best synonym will depend on the specific situation and the tone you want to convey.