Do you need to rinse vegetables that can be peeled?

It is redundant to rinse then peel garlic or onion. On the other hand, I do rinse carrots, cucumber and potatoes before peeling. The difference being that you actually remove the outer casing when peeling garlic or onion. With other vegetables you just shave off the very outer layer, often times not thoroughly.

I have never rinsed garlic or onion that I intend to peel, nor have I ever seen anybody do it. I will brush off soil stuck on them, but I never see that on onions or garlic from the grocery store. I suppose in some parts of the world rinsing garlic and onions would not be uncommon. If I ever saw it, I would wonder if they really have reason to believe their garlic or onion is that dirty, or if it's just a cultural quirk.

I rinse home grown garlic before peeling, but not bought garlic or onions. This is because my soil is very sticky, and so much clings to the outer skin that it otherwise gets everywhere when preparing it. If it's very dry, just brushing the dirt off also works.

If you do rinse a garlic bulb and don't use it all, you need to make sure it drys out properly and quickly, otherwise it will spoil.

While I don't always practice what I preach, in the interest of food safety, I would recommend rinsing any vegetable or fruits before peeling.

The reason for this is that when you cut into an unwashed vegetable or fruit, any contaminants on the outer surface are transferred to the part of the item you are going to eat.

While it doesn't happen often, some foods have been contaminated by E. coli, salmonella, pesticides, fertilizer residue, etc., when not rinsed first. In the worst cases people have become ill from it.

Garlic may be the exception as the outer peel is usually removed by hand before doing anything to the individual cloves. (Except when roasting and the top is cut off.) Onions could also be an exception if you are able to remove all of the outer peeling so that your knife will not go through it when cutting the onion.

The obvious is if you don't plan to peel.

I know this is extreme and I don't rinse garlic but even if you peel by hand you get cross contamination as you have handled the peel and peeled garlic. If you peel then cut one at a time that is a bit of cross contamination. A better practice would be to hand peel all then wash your hands before cutting. You could also then rinse the peeled garlic.

It is absolutely important that you rinse fruits and vegetables before consuming them raw, even if you are going to peel them!

I know this seems counter-intuitive to many people, since the "bad stuff" on produce (primarily bacteria—the pesticides and other residues aren't going to make you sick, they just aren't very appetizing) is on the outside, and you are simply going to peel it away. The problem is, during the process of peeling and/or cutting the item, it is almost inevitable that you introduce some of the bacteria from the outside into the fleshy interior—the part you are going to eat!

Is it necessary? Well, you probably aren't going to die if you don't do it. Only a tiny amount of bacteria will be introduced into the flesh of the fruit/vegetable by this process, so the chances are relatively low that it will make a healthy person extremely sick. If anything, you can expect mild food poisoning symptoms—perhaps so minor that you hardly even notice anything awry.

It also isn't particularly necessary to rinse produce that you're about to cook. Onions and garlic are both sometimes eaten raw, And beyond the vegetables mentioned explicitly in the question, there are cucumbers, carrots, etc., all of which are frequently consumed raw.

As someone with training in food microbiology, my family sometimes thinks I'm over-cautious. But it never hurts to be safe than sorry, especially when you're buying commercial produce. You don't have to scrub it if you're going to peel it, but if you have running water available (and most of us do!), it is always a good idea to rinse your fruits and vegetables thoroughly, while rubbing between your fingers.

According to this reference, unrefrigerated foods with peels (like onions and potatoes) are excellent bacteria incubators when peeled but not so while in peel.

My take away: you may not need to wash room temperature sold produce with peels before or after peeling, but you must consume them without delay.

Living on an ocean going boat, where water is at a premium, unless your veggies come covered in what cows leave behind, then the answer is probably no. If you have particularly dirty veg, which is to eaten raw, then yes, but on the whole, boiling/steaming/microwaving will kill virtually everything. We live in a society that is a bit mamby pamby and a bit of dirt wont hurt you - most of the time! Oh, and after over 100,000 ocean miles in a small boat without using refrigeration I do know a thing or two about this - we do not use any tins or packets onboard.