Multiplexing a 74141 Nixie driver with a MAX7219
There are several problems with your plan:

The MAX7219 outputs aren't TTL outputs, i.e. they are not directly compatible with the inputs of the 74141.
The 74141 has no storage, and no enable input, so you would drive all nixie digits with the same pattern, instead of an individual pattern for each.
The fact that you intend to use an individual 74141 for each tube indicates that you actually don't want to use multiplexing, since multiplexing is usually used to save drivers.

Multiplexing would imply that you use a common 74141 for all tubes, and drive the anodes separately, in a non-overlapping way. The MAX7219 digit outputs would be used for that, but they aren't compatible with nixie tubes, either.
You say you don't want to use transistors, that limits your options considerably. ICs that are designed to drive nixies are fairly rare these days.
You don't need to have an IC to do the multiplexing, btw., since it is fairly easy to do the multiplexing in software on the Arduino. So you'd be better off dropping the MAX7219, because it doesn't help you in any significant way. It is built for driving LEDs, and ill suited for driving anything else. What you need is suitable drivers, and the challenge is to find chips that support the voltages required by the nixies.