I had to clean 50 textiles after 9/11 because my apartment was filled with fine white dust from the collapse of the towers. A conservator would have cost more than $10,000 dollars and, the textiles weren't worth it. So I dry cleaned them and hoped for the best.
I asked the dry cleaner to use clean fluid, which he did, and generally, things came out fine. There was a bit of bleed on an Iban woven jacket and some embroidered stitches were roughed up a bit. (I ultimately learned that there was asbestos in the dust so anything used horizontally or heavily dusted was tossed).
I also dry cleaned everything in a closet that was hit by moths, which seem to LOVE goat hair. There wasn't much in that closet, fortunately, but cleaning worked fine. The things that I was reluctant to clean went into the freezer.
These days, I clean most things I buy in the field and, when I buy on eBay, I ask the dealers to clean especially large pieces before shipping, because it is SO much cheaper to clean things in, say, Uzbekistan, than in Lower Manhattan. These aren't great pieces, but it works.
For better pieces, I use a conservator on the moderate end of the price scale. Or, if the piece is small, I leave it in the freezer for 3 weeks, in case there are critters. This is NOT a full proof strategy, especially if your freezer is opened frequently and isn't that cold - but it is a technique people use.
None of this is what the experts tell you to do but, for the kinds of things one finds in SaPa, or if you have to do a lot of sturdy pieces in an emergency, it seems to work out OK.