You won’t, and airlines have no obligation to transport you on a specific plane. The airlines’ website most times lists what aircraft they are scheduled to use, but they can be swapped anytime if the need arises.

Most airlines typically try to purchase their fleet all from the same manufacturer if they can.

There's a lot of additional cost that goes into maintenance, pilot training, pilot availability, etc. that has to be accounted for if you're mixing aircraft from different manufacturers.

You can just look up the aircraft owned by an airline and it will give you a pretty good idea what to expect.

You can also go on flight tracker sites and just look at what aircraft are running the route currently, which would also be a good indicator.

There are quite a few airlines that do not fly Boeing planes (EasyJet for example).

When booking the aeroplane will usually be listed but you can also check flight history of the flight number. Of course the airline might still swap the plane at any time.

As mentioned in the other answers as a consumer you can try but you will have no guarantee of airplane type.

I do wonder if this fear of flying Boeing will spread to company travel departments?

Say a few of the really big companies in the world decide their employees should not fly Boeing. That support for this is being baked into booking systems and demanded from operators. Could Boeing ever recover?

kayak.com allows you to search by plane type. not sure to what extent they can guarantee that you'll actually be flying that type of machine though.