If the dropout protector was that difficult to remove, you need to check the dropouts for impact damage. While many times the protectors are tight, given that the tolerances for the plastic mold might be a bit off, it is very possible that the frame/box/fork was dropped. This would cause the dropout to close slightly.

This is not likely to be a safety issue, but why take the chance?

Does a normal axle fit easily into the dropouts?