I order 99.9% of the elastics I use from Sew Sassy. She has a page dedicated to latex-free elastics on her site. (And ALL of the rubber bands she uses on products are latex-free, which is nice.)
Years ago, the owner of Bra Builders told me that all of the elastics she sells are latex-free, but you should probably check with her before ordering.
Many of the elastics sold at Bra-Makers Supply are latex free.
Dritz is the elastic brand-name I find most often. So, I wrote them and got a list of latex-free elastics they manufacture. This list is from February of 2019, so it may be out of date.
Dritz Latex-Free Elastic
Dritz 9325W –3/4” plush back, latex-free stated on package
Dritz Products Not Containing Latex, but Not Stated on Package
9344 – 5/8ʺ Glitter Elastics, black, gold and silver – 40% Spandex/43% Metallic Yarn/17% Nylon
9346C – lightweight elastic, clear – 100% Polyurethane
9347 – 5/8” buttonhole elastic, black and white – 73% Polyester/17% Nylon/10% Spandex
9348 – 3/8” stretch lace elastic, pink and white – 19% Spandex/81% Nylon
9350w – 3/8” Non-Slip elastic, white – 31% silicone rubber/silica gel, 56% nylon, 13% spandex
9577 -1 ½” soft waistband elastic, berry, green, orange, purple and tile blue
9387 – 1” Fold Over Elastic, black and white – 90% Nylon/10% Spandex
9388 W– 5/8” double ruffle elastics, 20 SKU’s – 95% Nylon/5% Spandex
9389 – 5/8” Fold Over Elastic, 17 SKU’s – 85% nylon/15% spandex
9379 – ½” Ruched Elastic , 9 SKU’s – 83% Nylon/ 17% Spandex
9577 – 1-1/2” Soft Waistband Elastic, 5 SKU’s – 50% Nylon/ 35% Spandex/ 15% Polyester
9578 – 1-3/4” Metallic Waistband Elastic, 2 SKUs – 62% Polyester/ 27% Latex/ 11% Silver Metallic//11% Gold Metallic
Dritz Elastics Available through Walmart, Also Manufactured Without Latex
11346 – Lightweight Clear Elastic
11166 – 1” Fold Over Elastic
Babyville Boutique Brand Elastics, Manufactured Without Latex
Fold Over Elastics:
35040
35041
35042
35043
35044
35045
35046
35047
35124
35214
35258
35259
35260
35261
35262
35304
35305
Other Dritz elastic contain 25% polyester, 75% rubber and do contain a natural rubber latex.
This list is very helpful, thank you!