Do you need a table saw to build cabinets? Absolutely not.
Don’t believe me? We built all the cabinets for this garage workshop without a table saw. Yes, even the giant ones! Those ceilings are 11′ tall to give you an idea of the scale.

We cut all of the pieces for the cabinet bases using a circular saw and cutting guides. In fact, we couldn’t have even used our table saw if we wanted to. We have a small table saw that only cuts to 20.5” wide. Our cabinets were extra deep, so even the smallest pieces for the lower cabinets would’ve been too big for our table saw to cut.

Even if our table saw could have cut the boards wide enough, I still would have opted to use our circular saw for the main cuts. When using a circular saw guide, you can get extremely accurate cuts without having to haul a huge piece of plywood through a table saw.
From a safety perspective, and a laziness perspective, I would prefer to use my circular saw when cutting down large sheets of plywood.
This might be the shortest post I’ve ever written, but it’s because the answer is so cut and dry. No, you do NOT need a table saw to build cabinets.
If you’re planning to start a cabinet building company, then sure. You should probably invest in a cabinet table saw, but if you are just trying to build some cabinets for yourself, you don’t need one.
I will say, we did break out our table saw to build our shaker-style doors. We don’t have a router, so the table saw was our best option.
That said, you still don’t need a table saw to build doors. You can create flat panel doors, or create a shaker-style cabinet using a Kreg Jig or by gluing thin boards to the front and/or back of a panel to create the shaker look.