Are they banning people from trading the stock or trading the stock on margin? On margin would be reasonable, if the volatility of the stock becomes very high, the broker is taking a credit risk on its client it may not want (plus suitability consideration). It may also make sense to restrict access to certain stocks if they are deemed too complicated/dangerous to retail investors. But I doubt the suitability would be a function of a market movement.

Or is the platform assuming that its clients are doing market manipulation by coordinating on reddit to push the price up, and wants no part to a crime being committed.

Just speculating, but can think of some reasonable reasons.