Ran into this before.
The law says that you must have a car seat for the transportation that you listed. Newer shuttles do have seat belts, some older ones do not. If you call in advance or prearrange a car seat when making a reservation they can be provided by most companies. Not all companies though. Now for reality or IME, some taxis don't care and some will refuse you. You may be standing there looking for a taxi for an extended period of time (did that). If there are a lot of paxs looking for taxis, the taxis get selective.