Curl Rehab doesn't have the usual "protein", "hydrolyzed", or "amino acids" that are straight up proteins or pieces of a protein, but it does have herbal extracts. Any herbal extracts have trace amounts of protein, because plants contain a bit of protein. So, they can act like proteins for people whose hair is protein sensitive. See here
Also, if you don't want to shell out for a shower filter yet, you might try rinsing with distilled water first. If that helps, then opt for a shower filter.