I haven't pickled them but Joy of Pickling has a recipe for Pickled Snap Peas. It calls for white wine vinegar, water, pickling salt, a bit of sugar, snap peas, garlic cloves, 1-2 small dried hot peppers, tarragon.
In any recipe like that, the garlic, the peppers and the tarragon could be deleted individually or entirely.
I'd say dried red peppers are fairly common. They're usually found in pickling spice blends. Part of it is aesthetic. They add color to the jar. And part of it is heat, like any pepper.
But there's no reason to use it if you don't want to. Dried elements can be added or deleted at will in pickling recipes. Because they're dried they don't affect safety.
Sometimes, also, people cook the spices in the pickling syrup but then pull them out before pouring the liquid into the jars. That results in a milder flavor, as spices tend to get stronger the longer they sit on the shelf.
Also remember any pickle benefits from aging; the flavors mellow.
I was actually wondering if peppers are common to pickling, not common in general. I've never pickled before, you can probably tell. I think they would LOOK superb, but wonder if it makes them really hot. I suppose I could try some with and without.
I use peppers in almost all of my pickles (dilly beans, cuke pickles, carrots etc.).. it all depends on the peppers you use and your particular tastes. My family enjoys things with a little more kick ~ just not to the point of burning off tastebuds ;-)
Yes, they are common but not required. I sometimes use Jimmy Nardelle or some other sweet red variety as the color looks so pretty in the jars. I use that Pickled Snap recipe and we really like the tarragon. It is my DGD favorite pickled veggie.