I never peel ginger. I've not noticed any change in taste but I will add that I have not made ginger ale with it where the flavor is much more noticeable than when cooking a dish with a small amount of ginger in it.

When I make ginger syrup I don't peel the ginger and it's fine. The one advantage of peeling the ginger here is that you can snack on it when you're done. (you can probably eat the skin, but I don't think it'd taste great)

If it's being filtered out, I don't bother to peel. When it's part of a dish I do because the peel can be tough and unpleasant.

If you freeze the ginger and grate out with a microphone, most of the peel stays behind, and what doesn't isn't noticeable.

You'd probably want to wash it pretty thoroughly- it does grow (partially) in dirt, and who knows what goes on in a ginger factory.

I only peel if it's conventionally grown. I don't peel if it's organic. I always check the 'Dirty Dozen' list of the safest and most toxic produce and buy, 'treat', and eat accordingly. I buy organic as much as I can afford. Google 'Dirty Dozen' and see the list from your fave news provider. Pesticides and herbicides linked to loads of cancers and autoimmunity.

I buy a number of mobs @ the Asian Mkt because it's so much cheaper. Then, I use a serrated grapefruit spoon and scrape off the skin. I wrap them & freeze them and grate it on a rasp while frozen when needed. Works great.