Ethanol discolored yellow when stored with a rubber stopper. Forming fine white precipitate when added to water
It’s not easy to know unless you decide to throw the full set of analytical chemistry at your yellowish ethanol. But we do have a few clues.

It is most likely that something from the rubber stopper got dissolved in the ethanol. This solution turned out to be yellowish so we can assume the compound itself to be yellow to brown-ish. Dissolution either came by the ethanol soaking the stopper while the flask was lying down or by evaporation/condensation.

We also cannot determine from the information you have given what the precipitate is that forms when you add water. But my first guess would be ions from the water being less soluble in an ethanol-water mixture and precipitating. If that is the case, it would be made up mainly of sodium chloride. It could also be that some component of the ethanol is insoluble in water and precipitates out. Considering your alcohol is denatured, it might also be the additive that makes it undrinkable. However, once again there are too many variables and you need the full set of analytical chemistry thrown at the precipitate to find out what it is.

Most certainly whatever is happening is not a good indicator of anything.