Cell sorting is the workhorse of biological research and medicine. Cell sorters are commonly used to sort heterogeneous cell populations based on their intrinsic features. Raman-activated cell sorting (RACS) has recently received considerable interest by virtue of its ability to discriminate cells by their intracellular chemical content, in a label-free manner. However, broad deployment of RACS beyond lab-based demonstrations is hindered by a fundamental trade-off between throughput and measurement bandwidth (i.e., cellular information content). Here we overcome this trade-off and demonstrate broadband RACS in the fingerprint region (300 - 1,600 cm-1) with a record high throughput of ~50 cells per second. This represents a 100x throughput increase compared to previous demonstrations of broadband fingerprint-region RACS. To show the utility of our RACS, we demonstrate real-time label-free sorting of microalgal cells based on their accumulation of carotenoids and polysaccharide granules. These results hold promise for medical, biofuel, and bioplastic applications.