Are commercial VFR flights legal? I live in Southern California and was surprised to learn today that a local company is operating very short-haul VFR flights as an alternative to car commuting.

https://www.floatshuttle.com/

I can understand operating out of small airports to keep costs down, but flying VFR for a service like this seems unusual to me. Is this legal?
It depends on the operator's "opspecs" which are negotiated between them and the FAA. Generally in the US the vast majority of part 121 scheduled airline operations are required to be IFR, but plenty of part 135 charters are permitted to fly VFR. They may be subject to weather minimums higher than the general VFR limits.