The thing is your "Brewer" would make sense in most settings. The issue is if the player creates a custom background called "Astronaut" with Religion, Animal Handling, Thieves' Tools and Disguise Kit.Yep. If a player chooses their own background skills and tools and comes up with their own name for their custom Background, then they are playing by the default rules. If you, as a DM, disallow this, then you are not playing by the default rules. You are playing by your own house rules.
In other words, if a player invents a background called the Brewer and chooses Nature, Medicine, brewer's tools, and Dwarven as their proficiencies, then they are playing by the default rules. They're allowed to do that, and they don't need a DM's approval.
Of course, this it's quite possible that one of the standard backgrounds wouldn't make sense either: e.g. "sailor" in the desert, or "faction agent" where there are no factions.
Which is why every background, core or custom, needs to be run past the DM for approval.