Ivan the Crazy, welcome at CFC

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and thank you very much for your kind words (with one exception) about CCM2.
The setting for units not to move in mountain terrain is achieved by using the wheeled flag in the editor and setting mountain terrain to be impassable by wheeled units. Nearly all units in CCM2 have these settings with the exception of some special units, that you have mentioned, among them holy men, lawyers, monks, scouts, workers, leaders, supply shipments and the AI barbarian units.
From the landunits that can been built normally, warriors are the exception, as they can move across mountains and other terrain that is impassable for units with the wheeled flag, because the different warrior units don´t have the 'wheeled-flag'.
All warriors have this ability - even the warriors of the civ that is played by the human player. The reason for this setting is avoiding an advantage that is too big for civs with the expansive trait, that can start with scouts, and to avoid situations when the AI is producing too many early units, that have next to no benefits, when the starting location of a civ is surrounded by mountains.
About the spearmen: All different, mostly civspecific, spearmen in CCM2 have the wheeled flag, even the spearmen that are played by the AI - meaning they all can not move in mountain terrain without roads. The standard Civ 3 spearman in CCM2 is disabled for gameplay and this is the reason why this unit in CCM2 was not set to the wheeled-flag. So if Civ 3 standard spearmen appear on mountains in CCM2, I think, there was something changed in your CCM2 biq.
CCM2 was and is played a lot in the
CCM2 succession games, where every situation of those games was noted with meticulosity. We can be sure, that if such a situation would have occured in any of these games with an unmodded CCM2 biq, this would have been reported there energetically. In my many CCM2 games I have never seen such a situation, too.
So Ivan the Crazy, please post what spearmen (and may be other units) of what civs did these actions in mountain terrain without roads in an unmodded CCM2 biq (that for reasons of game functionallity in the C3C mainfolder must be named conquests) and I will have a closer look on that unit.