Can Ballistic Parachute Recovery Systems be safely deployed in a storm?
Manufacturers are going to have different opinions of this scenario, but this answer follows the opinion of Cirrus Aircraft in their flight manuals and CCIP syllabi for the SR2X airplanes.

First off, your best bet is to obtain a proper weather briefing prior to departure and obtain in-flight weather updates enroute so you can stay out of a thunderstorm in the first place.  The CAPS has very specific guidelines for operations as well as a maximum demonstrated safe deployment speed, depending of the model of aircraft.  The flight manuals for the SR2X aircraft all state that:

"However because the CAPS is expected to result in structural damage to the airframe and, depending upon adverse external factors such as high deployment speeds, low altitude, rough terrain and high winds, the CAPS deployment may result in severe injury or death to the occupants and its use should not be taken lightly".  

Barring that and you actually enter a thunderstorm which is so severe that it either causes departure from controlled flight or structural failure, there is a clause in the CAPS literature stating that if an accident is imminent, even if the acitivation of the CAPS is outside the demonstrated safe deployment range, it should be utilized and activated nonetheless.  The reason has to do with minimizing the amount of energy on impact and even a partially deployed or damaged CAPS is going to slow the aircraft considerably, increasing your chances of survival.  

Bottom line is that you did something stupid vis a vis a serious lack of judgment where a safe recovery is no longer possible.  Whatever happens in the next few minutes is probably going to hurt really bad; the only thing we can do is make every effort to minimize how badly we are hurt and minimize the chances that we are going to be killed.  Even an unsafe CAPS deployment in this situation is better than riding down to impact without.