Can BIP91 cause a chain split? BIP91 forces BIP141 signaling, the blocks that do not signal BIP141 will be rejected by those who are pro-BIP91.
The minority of miners that do not support BIP91 (and by extension BIP141), could start rejecting blocks of those who are signaling BIP141, thereby creating a different chain.
Is that a possibility both in theory and in practice?
The minority of miners that do not support BIP91 (and by extension BIP141), could start rejecting blocks of those who are signaling BIP141, thereby creating a different chain.
  Is that a possibility both in theory and in practice?


Yes that is possible, but unlikely. Since BIP 91 has a majority of the hashrate, I think it is unlikely that there will be a persistent chain fork. Rather what is more likely to happen is that there are short multi-block forks that are then orphaned and reorged out as the majority hash rate chain becomes longer than those forks.