No nether of them have the adventure class as it requires a manual shift from explorer to adventure and can't be gained through combat or any other natural method. Changing classes is not a simple matter and once you do so it tends to lock you out of others. That is what makes the MC so op is that he can change his and others class to any they have unlocked.
Roxanne's default class is Beast warrior and Sherry's is master blacksmith, both of this are race exclusive. And we also know for a fact Sherry is currently in her blacksmith class as she used item box, which only a few classes have access to (explorer, cook, blacksmith)
So to answer your question it would be fine if he entered after someone brought him there, he just cant after only he Sherry and Roxanne came through the portal as none of them have the skill that was seen used.
Also if they check his ID and a guard happens to recognize him later as he come through the portal they will expect him to have changed to adventure from explorer. This would lock him into keeping adventure as his main class which would hurt a lot as his bonus points total is based on his first set class, so he wants to keep explorer his highest level as first, and if he has items in his item box (explorer has the highest slot limits) he can't swap explorer around class order wise. So he would want to swap back, but if he is id as a adventure and later as a explore it would record him as having quite being a adventure back to a explorer. This is something others can do, but it permanently locks adventure. So if that gets noted down it could be recorded that he can't be a adventurer. So there are a ton of reasons why he is warry of id checks. Its one thing if the slave merchants see, as they don't see him fight or really keep tabs on what he can do. But the knights are another story, he doesn't want them knowing his class as they may question why he can do certain things, namely why he can warp.
This city is a pain to him do to how strict their security is, and how he has to warp in front of the guards who will id him.