Am not an expert at all, but I think that looking for 'non-bleach alternatives for linens' will generate some suggestions and reviews. I occasionally use The Laundress whitening /stain remover, it's a bit pricey tho. I did not use it for super precious delicate things, so I cannot say much about fabric safety. If it's a special garment I'd do a test on a small hidden patch.
@artemis Thank you!!!