I'm going to assume the Zenith carb in question is a CD4T as fitted to the Triumph 1500 engine used in the Midget once the A series engine ran out of stretch.
The plastic parts that I can think of on the carb are on or in the autostarter, a restrictor for the hose that goes to the carbon canister, and the tamper-proof cap that might still be on the throttle bypass valve. I suppose you could say that the float is a plastic part, and depending on the exact year of the carb there may be a plastic plug in the float bowl. That's a remnant from the days when the mixture jet was adjusted through the float bowl, Zenith carried on the casting for a long time after that hole was necessary because it was a great way to set fire to cars when the o-ring started to leak.
None of those parts are part of a rebuild kit and don't normally need to be replaced. You need to keep carb cleaner away from them as most brands of cleaner will eventually ruin plastic parts. You're better off using something like PineSol as a cleaner anywhere near plastic stuff, especially on the autostarter where some parts really should be left in place.
The big item that needs to be replaced as a preventive maintenance measure is the diaphragm. Zeniths used a diaphragm to control the air piston to avoid infringing on SU patents. A lot of people whinge about them, but they are cheap and very easy to change, job can be done with the carb on the engine, four screws to take the top cover off, four screws to remove the diaphragm retainer. Those screws can be tight, and they are Pozidriv screws, not Phillips. A Pozidriv screwdriver will do the job without much fuss, a Phillips screwdrive will just chew the screws up.
The diaphragms are available as a separate item for about $10, the Zenith part number is B20924. You don't need to buy the rebuild kit to get a spare. I have no idea if Moss sells them as a separate item, but both Spitbits and the Roadster Factory have them and it's a good idea to carry a spare as your car won't run very well if the diaphragm develops a tear or pinhole.
If there's some other part that you are concerned about, email me a picture of it.
A lot of people badmouth the Zenith carbs because they are more complicated than the SUs on the earlier cars. That's because the Zenith had to cope with emissions requirements and turned out to be easier to modify than the SU.
