"The accurate and persistent balancing of this class isn’t guaranteed."
The Goatperson is the secret monster class, acquired by unlocking the Goat Glade (available to early supporters or as DLC on Steam). It is a dangerously experimental class, based on short-term and sometimes extremely short-term decisions.
Exploring a tile costs food, which takes up a small inventory space for your whole supply. Killing an enemy gives 9 food, and, more to the point, exploring without food damages you until you GET FOOD or DIE. Each tile uncovered will deplete 1 food. As you might be able to tell, this adds up really quick. This obviously is meant to limit exploration, as no food is consumed by going back over uncovered tiles.
The Goatperson will randomly worship a new god out of the 3 that have altars in the dungeon (or 2, if you haven't unlocked enough gods yet) upon level up. The no-desecration aspect is simply done so that you can't escape this change by destroying the other altars.
This trait is designed to severely limit the strategies that one can implement, as it is impossible to be sure when you will be forced to worship one god instead of another. The Goatperson will always change to a different deity on each level-up, and will never remain with the same deity.
The fact that the Goatperson does not heal upon level up completely torpedoes mid-fight level-up strategies, and makes progression much, much more difficult. While you can still heal mid-fight by converting, the increasing conversion cost makes this rather costly, and severely limits supply. The exploration phase is also much more difficult, because you cannot rely on leveling up to heal you. Therefore, the only ways for your character to heal at all are by exploring(which is limited by your food supply, which is only replenished by killing monsters), using glyphs, converting items, using potions, and taking god boons. All of these are in limited supply. Exploring becomes extremely conservative, as you will be forced to heal every wound by using consumables. By the time you reach the boss, it's likely that you won't have any way left to heal yourself.
The last feature (gold instead of boss trophies) merely ensures that you cannot use the Goatperson for quest progression. It remains to be seen if the amount of money dropped is equal to the value of the trophy that would've dropped instead. If so, this could be useful, as it would allow one to get around that fact that a trophy's price drops the more that you collect that particular trophy.
Simply put, this class was carefully balanced to stack the deck against the player as much as physically possible without making it completely impossible to win.
Technically, it's possible to win with this class. Impossible is the next door neighbor, though.
This is a challenge class. If you can beat a dungeon with this class, then you're either inordinately lucky or an absolute master at this game.
Heck, it'd be close to a miracle to beat an easy dungeon with the Goatperson.
For those still not deterred, it is worth noting that nowhere does the Goatperson's features limit item use. The only way that I could see this class succeeding is by loading down with as many powerful items and potions as possible and using them to somewhat offset the Goatperson's deliberate flaws.
Good luck. You're going to need it.