S. coeruleoalba is currently listed at Lower Risk in the IUCN - Red List. It is further categorized as being "Conservation Dependent," meaning that the species is in a taxa that is the focus of a conservation program. Without a conservation program, the striped dolphin will qualify for a threatened/endangered status within five years.
Habitat degradation, commercial fisheries, and killing dolphins for their meat all contribute to striped dolphin population declines.
US Federal List: no special status
CITES: appendix ii
IUCN Red List of Threatened Species: least concern