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First, it can leave particles on the way down to the stomach. Second, many molds (and fungus) release toxins, when broken down, which is what is dangerous. This isn't the case of every mold or fungus though, the fungus, penicillin is is the same type of fungus found on your "moldy" bread, there are many strains of fungus and its mostly the breaking down part inside of us that's the bad part, not the fungus itself. (Not always the case of course).

There are also plenty of virus and bacteria which are resistant to stomach acid for long enough to make it through to the rest of the body.

Acid is not magic, despite what spy movies and the like would have you believe it doesn't just dissolve whatever it touches immediately (if it did that would be bad for your stomach for example). The acid in your stomach is for breaking down food. It will also affect other things obviously but not everything. Depending on what you ingest it can be harmful before it gets to your stomach, inside your stomach, or after it passes through your stomach. It takes time and effort (churning) for your stomach to even break down the food you eat, and even that it doesn't do completely. Take corn for example, the shell of a kernel of corn can survive the entire digestive process and pass through into your stool intact if its not chewed well enough and pre-broken down. Our stomachs aren't the friendliest environments around, but they aren't the most hostile either.

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Acid isn't able to digest your food entirely. Some digestion happens After the stomach. Plus, thé more you eat, the less acidic your stomach will be.

And i'd finish with the fact that pathogens can be so resistant to acid that there are examples of pathogens living in your stomach. Like Helicobacter pylori.

Stomach acid doesnt break down many (possibly most) of the toxins that bacteria and mould produce, which can already be at high concentrations in contaminated food. So whether or not the bug survives or not doesnt help you.

Bacteria that cause gastrointestinal infections have various ways to survive digestion. Salmonella for example relies on being consumed at the same time as food and being digested in high numbers, when you eat a meal, the food offsets the pH of your stomach, making it closer to neutral. Other bacteria have specific protective mechanisms against stomach acid.

Also stomach acid isnt all that acidic, you would know when you throw up your tongue doesnt dissolve away or anything, its not equivalent o the acid used in acid attacks for example.

Sure. Acid will kill most bacteria. Kinda of why probiotics don't work. But not all bacteria. Kinda why probiotics work.

Other problem is that mold and bacteria produce toxins. So it's not only that you ingest the lifeforms but also the toxins they produced. Acid does not neutralize most toxins.

Most of the digestion happens after the stomach, really, with pancreatic juices and the brush border carrying lots of enzymes. And some also happens before the stomach.