"As engagements dried up, the Weavers disbanded, though they reunited occasionally in the mid-1950s. After the group recorded an advertisement for Lucky Strike cigarettes, Mr. Seeger left, citing his objection to promoting tobacco use."
I know Pete didn't like smoking at his performances but is that really the reason for his departure from the Weavers at that particular time?"

Actually Pete's departure was a long time coming. In Las Vegas, at a crucial point in the career of the Weavers, Pete Cameron, the first official manager of the Weavers (Toshi was never given credit) decided that they should limit their activities to safe appearances but Pete wanted them to sing at a union rally but the other members apparently objected to that.
Pete was incensed and well the story is that he broke a glass table in the hotel room where they were staying. It's possible that it happened because Pete was human and had a rare temper as we all do. I don't blame him, however for being pissed.