What neutrality actually removes
A market neutral strategy holds offsetting long and short exposure so that the direction of the underlying market largely cancels. What is left is intended to be the return of the manager's selection, spread or relative-value judgement, separated from whether the asset class went up or down.
That is a precise claim, and it is worth reading precisely. It says that one exposure has been removed. It says nothing about the size of the remaining exposures, nothing about leverage, nothing about liquidity, and nothing about whether the position can be exited. "Neutral" is a description of a hedge, not a description of risk.
The word does a great deal of work in a conversation, which is why it is worth being pedantic about it. An allocator who hears "market neutral" and infers "low risk" has substituted one exposure for the whole risk profile.