That's my reading of the vehicle code anyhow. I Am Not A Lawyer, but read on:
The child seat laws are defined in the California Vehicle Code in section 27360 which is titled Child Passenger Restraints: Requirements. It starts like this:
27360. (a) A parent or legal guardian, when present in a motor vehicle, as defined in Section 27315, may not permit his or her child or ward to be transported upon a highway in the motor vehicle without properly securing the child or ward in a rear seat in a child passenger restraint system meeting applicable federal motor vehicle safety standards, unless the child or ward is one of the following:
(1) Six years of age or older.
(2) Sixty pounds or more.
Where it gets interesting is when you follow the trail of "when present in a motor vehicle, as defined in Section 27315." Section 27315 defines a motor vehicle like this:
"motor vehicle" means a passenger vehicle, a motortruck, or a truck tractor, but does not include a motorcycle.
Wow, first surprise. It's legal to carry your child on a motorcycle. Good to know. Wouldn't recommend it. I wonder about sidecars?
Then there's the bits specifically about taxis:
This paragraph does not apply to the operator of a taxicab, as defined in Section 27908, when the taxicab is driven on a city street and is engaged in the transportation of a fare-paying passenger
However, it's not all loosey goosey in the cabs, folks!
The operator of a taxicab may not operate the taxicab unless any passengers six years of age or over or weighing 60 pounds or more, in the front seat are properly restrained by a safety belt.
Ok, so that means your 6 year old can sit in the front seat of a taxicab without a car seat, but better put on that seatbelt. However, the rear seat needs to be filled with children under 12 (and presumably under 6) according to Section 27360-c-1-E:
For purposes of subdivisions (a) and (b), and except as provided in paragraph (2), a child or ward under the age of six years who weighs less than 60 pounds may ride in the front seat of a motor vehicle, [...] under any of the following circumstances: [...] (E) All rear seats are already occupied by children under the age of 12 years.
That first set of ellipses is important. Here's what I removed: if properly secured in a child passenger restraint system that meets applicable federal motor vehicle safety standards. Whoa, you say, what are you trying to pull!? Well, as I read it, the taxicab-ness of the vehicle has already excluded the car seat requirement, so the logical re-reading of that section in terms of a taxicab is the six year old can sit up front as long as they wear a regular seat belt. Isn't law fun? No wonder lawyers are such a happy lot.
There's actually another portion that covers any driver's liability, including a taxi driver. 27360-b states that any driver is not in violation of the law if the child's parent is also in the car (and not the driver). So if you are willing to take your child in a cab without a car seat in the first place, the taxi driver can't reasonably refuse you on legal grounds even without the special provision for taxicabs.
What about trolleys and busses? Obviously you don't need a car seat in these motor vehicles. I'm not sure if they are excluded because they are not specifically defined as motor vehicles in section 27315? When I first read through these sections of the code a few years ago I swear there was a provision that excluded any vehicles that lacked seat belts, so that covered busses and trolleys. I can't find that provision now though, maybe the law changed?
I'd love to get some feedback from a real expert on all of this, any lawyers want to comment?