I just read this question on Quora about distilling during pre-industrial age, which reminded me about multiple discussions I have heard or read during the years about whether the fermentation process used to produce alcoholic (ethanol) beverages produces methanol.
As far as I understand it, yeast, sugar and water results in ethanol. A similar process to get methanol would require you to (destructively) distil wood (methanol is also called something like wood alcohol in many languages) and since you usually don't include wood when making beverages, there should be no methanol in the result.
Furthermore, non-hard liquor like beer and wine do never have a "methanol problem" although, especially wine(-like liquids) often is used as a base when producing hard liquor. Besides, when binge drinking, you typically drink similar amounts of pure ethanol independently of if you drink wine or hard liquor.
My guess is that a reasonably controlled fermentation process of grapes/barley/fruits/grain/etc doesn't result in any noticeable amounts of methanol and if you distil it and keep everything and mix it good it is as safe as drink as home made wine and beer. The problem with methanol, my guess again, is that people in the "moonshine business" sometimes dilute the result with methanol because it is cheaper.