There are two problems with your question. The first is the near-universal assumption these days that ketchup refers to a tomato condiment. The second is that it’s almost as big a production to make mushroom ketchup as it is to purchase it (in this country, at least).
Historically, ketchup has been a condiment based on just about anything. The origin of the word is said to date to 17th-century China, where a spicy pickled fish sauce was called ke-tsiap. The sauce found its way to England, where it evolved in many directions, with the addition of anything from mangoes to walnuts to mushrooms. It wasn’t until after ketchup made the voyage to New England, that it featured a tomato foundation, and became the popular sauce for which the French now tend to mock us.
Mushroom ketchup is more familiar in Britain than here, but don’t be daunted. You can find it available online (barely), and we have turned up several recipes, including one from The New Joy of Cooking, which describes it as an “English condiment for robust meats and game [that] is a thin, pungent, deeply flavored sauce.”
Note: Now, it may shock some of our readers to hear this, but for the recipe for Mushroom Croustades, which inspired this whole mushroom ketchup question, and which calls for a modest 2 teaspoons of the stuff, we might not embark on the multi-day journey to produce it. We would buy it online, or might ignore that line in the recipe entirely, or use a half teaspoon of olive oil, a half teaspoon of vinegar, and a teaspoon of beef stock (if we didn’t care about the vegetarian origin of the recipe), and hope for the best. It would not be the real thing, but occasionally we live on the edge.