[...] because if a writer enters an infinite loop while writing the shared data, that will stop progress in any other algorithm [...]

Even if you have

  while (true) { sharedData.writeWaitFree(randomData) }

all other threads will be able to continue. Whether the result will be of any value will depend on the use case.

If, on the other hand, you mean that some threads will enter an infinite loop inside of a read or write operation, then you have a bug in your wait-free algorithm and all bets are off. But we would generally assume that the implementation is good and the erroneous behavior is external.