I am running Curse of Strahd at the moment and one of my players is using a Bugbear, which is causing me some challenge.
The module specifically states:
Barovians thus react to nonhuman characters the same way most humans in the real world would react to elf, dwarf, or half-orc adventurers suddenly walking the streets. Most such outsiders are scorned, feared, or shunned
How can I play this without locking this character out of almost every interaction or town? Specifically there is a fortified town which I can't see letting in what they would clearly see as a monster.
Just trying to persuade every NPC to not be scared sounds like it is going to get boring (and the character has -1 charisma), be that a simple roll or a proper RP interaction. Equally I don't want to just ignore it, or play simple lip-service to it.
Frame challenge: why wouldn't you lock this character out of almost every interaction in town? Even in a progressive city like Waterdeep, I wouldn't expect to see bugbears in the open interacting with "normal" citizens. From Volo's Guide to Monsters (p118, under Monstrous Adventurers):
Don't be afraid to push things to an extreme. An orc character might
have to venture into town in disguise or remain in the wilderness, for
fear of imprisonment or mob violence. Be sure to talk to the group
about how such characters can expect the world to treat them.
How it went in our campaign: despite my DM's warning, I played a tiefling. When in Vallaki, my character always had his hood up. The mayor also had really poor eyesight, which helped us at first. During a festival, however, the paladin raised a stink about treatment of some villagers. It was at this time that the mayor took a closer look at my character, and saw the horns + red skin. Our entire group was chased out of town (this was played as a combat, not just RP). Shortly after, we helped a new mayor take over the town. Regardless, my character stayed out of that particular town for the rest of the campaign. Our party did not have any issues, at least not with our own race choices, anywhere else in Barovia.
My thoughts (as a player): I could have used Alter Self, or at least Disguise Self, to improve situations for myself in town. This campaign definitely taught me to play more cautiously, and less recklessly. Later in the campaign, I rolled a new character. This time I went with human, instead of tiefling.
Unsolicited advice: Before any campaign starts, please be sure to at least skim through the campaign book twice. After that, have a session 0 where you tell your players what to expect before they finalize their character choices.
I have run this campaign a couple times now and have run into this issue. I have had Tabaxi and Minotaur players and handled them by having the populace assume that they are "mongrelfolk".
Found in Krezk in the care of the Abbot, Mongrelfolk are cursed people that exhibit all manner of beastly deformities.
In your case in particular, bugbears make a good candidate for this treatment. Mongrelfolk would be known the the populace of Krezk, and the leadership of the other communities, with their populations probably having heard of them.
This allowed the players to access cities, but still be treated with distrust until they secured the assistance of the community leadership.
I personally have found it helps to have villagers treat the creature like a lion or a bear. If free, they're an object of abject terror, but if contained they can be managed.
If free, have people act just like they would with a large predator free in a city.
Most people will stay far away, a few bold people will poke them, and concerned citizens will call local militias and the guard to handle them. This may take a while depending on how concerned they are.
Per the module notes, many will stare at the player. The intensity of the staring will ramp up until violence starts.
The way Barovians deal with strangers can be unsettling to newcomers. Barovians have a tendency to stare openly, in silence, thereby expressing their disapproval of anything that isn't familiar to them. Barovians aren't talkative with strangers, to the extent of being pointedly rude. Most Barovians have violent tempers that boil up through their customary silence when they are provoked. They also have a social cohesiveness (thrust upon them by their weird circumstances) that can make them act together against outsiders if a Barovian and is mistreated.
Local guards will encourage and suggest you keep your pets leashed.
If there are humans in the party, the Barovian guards will likely assume that they have control of the bugbear. They will suggest you buy or make a leash so that you can ensure your pet doesn't rampage, and hold the players responsible for any bad behaviour.
Good behaviour may win people over.
If the PCs do heroic things with the aid of the bugbear that benefit the civilians, or the bugbear manages to do cute and adorable things, they may be able to sway people so they can go in public more.
In my games this worked well, since people know how they would react to a rabid animal but most wouldn't care much if elf adventurer cosplayers wandered around.
Every character gets to interact with those of a similar social status. The bugbear may have to stay at the low-class inn, or sleep outside of town and miss out on the meeting with the adventure-giver. But they get to interact with the other low-class folk also forced to stay there.
Visiting rowdy hunters with gossip. A farmer yelling "hey you, monster -- can you kill spiders? We got a big spider problem if you want to make some money". A cleric of an unpopular god not allowed in this town who knows about an evil ritual in two days. Other patrons notice the bugbear drinking, are amused, start a drinking contest, ending with them all on a first name basis. If they come back, they'll receive a warm welcome at that inn. At the very least, they get to watch goings-on outside of town -- a lot of people coming from the east have been robbed by bandits.
Put another way, if you have several mini-adventures you can give them a hook for one. With one big adventure you can give them a clue. Or you can just give them something fun to do. If everyone is doing 5 minutes of town stuff, this fits right in. If the main group met someone for 15 minutes, 5 minutes with the bugbear gives them time to make plans. Always having to cut to the bugbear may get old, fast, but it won't be that often and you can always keep it short "the rowers in the bilge deck tell you they once saw a minotaur pirate captain".