Phoenix…BOTH the Brocade and the Linen, DON’T LIKE WATER, as far as I know as a Fabric Person that I am. There are Cleaning Products on the market that’s a Powder Like Substance, or there USED to be, it’s been awhile since I needed it…then you use a soft toothbrush, work the powder in, and then with another soft brush or rough washcloth wipe the powder away.
DO NOT USE WATER on brocade, DO NOT USE WATER on Linen, or ANYthing with water in them, they might cause WATER SPOTS!
However, IF You’re going to USE water and a mild detergent, do the WHOLE shoe and dab, dab, dab with an ANOTHER, clean, and absorbant cloth, and then let what’s still wet, air dry, or USE the AIR ONLY Setting on a Blow Dryer and Dry Evenly…but I warn you, water’s not recommended.
SOME stains will NOT come out, like ’’yellowing’’ stains on lighter silk, voile, or brocade…etc.
Try this method, too…Spray some CHEAP Hairspray on a CLEAN CLOTH, rub it on the stain, IMMEDIATELY use another clean cloth to dry it off. A Hairspray like Aqua Net gets INK stains out of cotton, but I don’t know if it works on shoes made of Brocade, Silk, or Linen? I don’t recommend this method, so you try it on your own.
BEST method is to seek a DRY CLEANING product.

I have had good luck with the eraser block or magic eraser. It does a great job w/o water. You can buy them in the market cleaning isle.

Cleaning fabric on shoes or handbags is not an easy task nor really suggested unless taken to the professionals to do a thorough clean up job.

The best way I clean my soiled fabric tenni shoes (like converse) after a weeks’ athletic workout is to place into the upper top level of dishwasher. The hot steam and water gets them super clean especially if the fabric is white or bright. Then I leave them on patio couple of days to dry from direct sunlight and repeat the process once every 6 weeks

but that is not a suggestion for cleaning fabric shoes that are naturally stiff and have leather (mine are all rubber soles).

Sorry I could not be better help but I am also curious to read what others might suggest.

I would take them to a dry cleaners that also deal with shoes.
I did just read that some people use baby wipes or a Mr. Clean sponge on their shoes. One person suggested putting shoes into a pillow case and then put in washing machine. I don’t think I would do that though.

First vacuum them with a above-floor attachment, then brush with a clean, soft-bristled brush, then vacuum once more.

best think to use would be Picrin from a local dry cleaner if they will give you some, or they might possibly do it for you.

Dry sprinkle in carpet cleaner has worked for me in the past. Just follow the directions, then vaccum out. Magic erasers have worked as well.

I’ve used baby wipes on small stains on furniture fabric with a lot of success. The idea was to use minimal moisture. It should work on fabric shoes as well and might be worth a try.

An older German lady I once knew used a piece of stale brown bread to wipe this type of fabric on shoes, picks up both dirt and grease pretty well.

Test on an inconspicuous area, stay away from heat/flame; years ago my mother used to clean all types of fabric purses, shoes and clothing with lighter fluid. Scares me to death, but when all else fails, I have used it on a few things with success. Oh! Use in a well-ventilated area too. The fumes are fierce.

Use Mr Clean magic earaser, it works without marks