Vinegar in the rinse cycle hasn't fixed my musty towels after three washes Question

You're doing it wrong, but the tip is also oversold. Two problems with what you've described.

First, the vinegar is going in with the detergent still in the water. Detergent is alkaline, vinegar is acid, and they largely cancel each other out, so half a cup of it in a full drum of soapy water is doing very little. If you use vinegar at all it needs to be in a rinse with nothing else in the machine.

Second, warm isn't hot enough and vinegar isn't the right tool anyway. What's in the towels is a mix of body oils, detergent residue and bacteria that live in it. The thing that actually removes it is oxygen bleach, sodium percarbonate, dissolved in genuinely hot water.

What worked here: wash the towels on the hottest cycle the machine offers with a scoop of oxygen bleach and no detergent, no softener. Then a second normal wash with a correct dose of detergent. Then dry them completely, straight away. Mine came back from that and haven't smelled since.

Also look at how fast they dry after use. A towel on a hook in a windowless bathroom stays damp for eight hours and that's plenty of time for the smell to develop. Spread flat on a rail rather than bunched on a hook made more difference for me than anything I did in the machine.

Check the machine before you blame the towels. Front loaders hold water in the door gasket and in the drain filter, and after five years both are usually revolting. Peel the rubber seal back and look in the fold, and empty the filter at the bottom front over a towel you don't like. If either smells, everything you wash is going to pick that up.

Vinegar does have a use here, just not the one it's famous for. Running an empty hot cycle with two cups of vinegar and nothing else strips soap scum out of the machine itself. As a fabric treatment in a loaded wash it's mostly folklore.

Add more detergent, that's what deep cleaning means. Two caps minimum for towels.