The change into wet weather gear is triggered when the weather crosses the line into "storm conditions," determined IIRC by wind speed and the level of precipitation (if any). The same thing also determines whether or not you can use your guns.
The All Weather Guns mod changes the definition of "storm conditions" so that no matter how bad the weather gets, it never triggers the game to disallow the use of guns. However since the same trigger is used to put your watch crew in their wet weather gear, that never happens either.
So, there's no "conflict" as such, it's just that both things are tied to the same trigger: how the game defines what constitutes "storm conditions." So it's a trade-off, either you get guns in all weather, or you get a watch crew that puts on oilskins when the weather gets bad. You can't have both.