See, since you are pounding out loyalty to the Kaiser into their ears it does. They have been told they are supposed to be loyal to the Kaiser... Now there is a congress they are supposed to be loyal to. A democratic congress has just popped out of no where, and I don't imagine an army which you have drilled loyalty to the Kaiser into would just be okay with something popping up which limits the Kaisers powers and has the cheek to put it on his level. It makes sense that this group that's called the royalists would also include militarists, who are often very patriotic... Not in the least because this group includes those.dissatisfied with the name change, which would likely be the mark of patriots and militarists
Being extremely loyal to the emperor but at the same time not having royalists among them is kind of mutually exclusively. The army is going to have its own political views and their officers are likely royalists. I should point out in this period of history, officers were mostly nobles, and that being "raised from the ranks" was taboo and any of these low born officers would be put under constant scrutiny and abuse, disproportionately punished for their failures to the point they might find themselves back in the ranks from a single battle or called traitors for any failures or just circumstances of the battle that weren't in their control. Like with all society, the nobles found themselves in a considerably better position and being an officer became like the old boys club, particularly in the higher ranks, IE: Generals, field marshals. And if anyone tried to take this away from them then they went absolutely nuts, and they had a huge amount of influence... Particularly in the army and government. 

Because of these social divides at the time, and the general role of nobles, it does make sense that the royalists have considerable influence in the armies. The military its self has "trouble" written on its forehead, and will be strongly supportive of status quo, wishing the emperor to be an unopposed force and wishing the Lance Empire to retain its name... if that means conquering Numburg, they're probably fine with that