Some Boy Scouts may have used boondoggles; the troop I was in back in the ‘50s in Chicago wore neckerchief slides.

aldi’s post reminds me of the 1960s/70s TV comedy All Gas and Gaiters the name of which I never examined at the time.

gaiter [ˈgeɪtə]
n (often plural)
1. (Clothing & Fashion) a cloth or leather covering for the leg or ankle buttoned on one side and usually strapped under the foot
2. (Clothing & Fashion) Also called spat a similar covering extending from the ankle to the instep
3. (Individual Sports & Recreations / Mountaineering) (Clothing & Fashion) a waterproof covering for the ankle worn by climbers and walkers to prevent snow, mud, or gravel entering over the top of the boot
[from French guêtre, probably of Germanic origin and related to wrist]
gaiterless adj
Collins English Dictionary – Complete and Unabridged 6th Edition 2003

No mention of ecclesiastical use. Gas must mean windbaggery. Maybe they were originally made from alligaiter skin.

Would this be the equivalent to the gaiter of the British Army?

No, a blousing rubber isn’t a covering of any kind. It’s an elastic string (if you don’t have one, a rubber band will substitute) around which you drape some of the material of your trousers so that it forms an even line over the top of your boot. The equivalent to the gaiter in the US Army would have been leggings, but these went out in the 1940s (maybe early 50s) and were way before my time.

Regarding Boy Scout boondoggles. For me the more common term was neckerchief slide too, but boondoggle was not unknown.

Wikipedia looks sound on clerical gaiters:

“Gaiters formed a part of the everyday clerical clothing of bishops and archdeacons of the Church of England until the middle part of the twentieth century. They were made of black cotton, wool, or silk, and buttoned up the sides, reaching to just below the knee where they would join with black breeches. Gaiters would be worn with a clerical apron, a type of short cassock reaching to just above the knee. The purpose of this vesture was originally practical, since archdeacons and bishops were presumed to be mobile, riding horses to various parts of a diocese or archdeaconry. In latter years, the clothing took on a more symbolic dimension.”

You can read all about bishops and gaiters, complete with pix of same (both bishops and gaiters) at this wonderful site here. There’s a bit about the association of bishops with windbaggery which gave rise to the expression “all gas and gaiters” here and a bit about the nickname of the sports team from Bishop’s University in Canada, “the Gaiters”, which comes from the legwear and not the reptile, here.

British Army gaiters replaced the puttees British and Commonwealth soldiers wore in the First World War, and which were, I believe, even more widely hated by the soldiers than gaiters …

Gaiters formed a part of the everyday clerical clothing of bishops and archdeacons of the Church of England until the middle part of the twentieth century. They were made of black cotton, wool, or silk, and buttoned up the sides, reaching to just below the knee where they would join with black breeches.

A certain bishop, after a lifetime of virtue, finding himself alone one day in a strange town far from home, fell victim to temptation and allowed himself to be picked up by a lady of pleasure. On their arrival in her room she invited him to take off his clothes. He went into the bathroom and stripped off --- but catching sight of himself naked in the mirror, put on his gaiters, feeling that in this way he might retain some shred of episcopal dignity. Thus garbed, he went back into the bedroom.

Young lady: “Goodness! what are those things?”

B. “They’re my gaiters.”

Y.L. “Whatever are they for?”

B. “To remind me that I’m a bishop.”

Y.L. “A bishop, are you? Fancy that. From the size of your balls, I’d have taken you for a canon.”