Sometime on an early 90s evening I stepped onto a Framingham Local at BOS. It went one stop to BBY and we were told by the conductor to get out as CSX or Conrail dispatchers were honoring some strike. No announcements at South Station or communication from the conductors that the train would only go one stop. I was pissed, it really screwed up my commute. Only affected one or a few days though.
At the time, Amtrak was running Commuter Rail, and dispatching the NEC and South Station to BBY on the Framingham Line. I believe Amtrak workers are federal employees and cannot strike or join in secondary boycotts. But Keolis is a private, unionized company. If a national strike is called, they would be pressured to honor any picket lines. Maybe there won't be picket lines in the Boston area due to lack of freight operations, but the MBTA and PAR/CSX have a combined dispatch center. And [OT] but the Amtrak Downeaster runs over track dispatched by PAR/CSX, the Boston section of the Amtrak Lake Shore Ltd. runs over CSX dispatched track west of SPG
I believe secondary boycotts are allowed in the heavily regulated railroad industry, (transportation in general?), but prohibited in most other industries.
I think it unlikely to affect MBTA CR, but it is possible and has happened before.