Lego Pneumatic Engine: Possible Damage from Baking Soda and Vinegar?
I see two main problems that need to be adressed here.


Intrusion of liquids into the pneumatic system
Intrusion of solid particles into the pneumatic system


To filter out solid particles, namely baking soda, a fine mesh could be used, either alone or in multiple layers.

To get rid of droplets, some absorbing material such as cotton could be inserted before, after or rather between the layers of mesh.

So if we can suppose that the bottle will have an exit point that is always clear from the liquid-solid phase (based on your comment "with hose connections in the cap"), we can imagine the following filter system built inside a small diameter tube (like a plastic straw), where # denotes layers of fine mesh fixed inside the pipe, capable of holding back both baking soda dust and the loose cotton swabs:

 ________________________________________
/                                        \
|                                         \
|                                          \
|                                           \___
|                                               |
|            #cotton#cotton#cotton#cotton#======+
|                                            ___|
|------------------------------------------ /
|    o     8      O   Ö    *     0    .    /
|  °    vinegar + baking soda   :    ö    /
\________________________________________/



Or if you need to fill the bottle more than halfway, but can ensure that the sloshing will not reach the top of the laying bottle, then you might be able to use a doubly-bent straw:

 ________________________________________
/                                        \
|        #cotton#cotton#cotton#cotton#=\  \
|                                      \\  \
|                                       \\  \___
|----------------------------------------\\-----|
|  :         *           ö                \=====+
|       o      Ö    0        8     O    .    ___|
|   °                 Ö                     /
|    o     8      O        *     0    .    /
|  °    vinegar + baking soda   :    ö    /
\________________________________________/



But as MaxW has noted on your question over at Chemistry.SE:


  You won't get pure CO2 out of an aqueous solution. There will be water vapor in the CO2. 


So your metal parts will definitely be exposed to a (probably highly diluted) carbonic acid, that "can corrode, rust or pit steel but the extent of those effects depends upon the chemical composition of the steel. Stainless steel, in contrast, resists general corrosion caused by carbonic acid." (Source)

How fast of how much will the parts be corroded? I can't find a definitive answer for that, but in the end, it all comes down to three, highly variable factors:


The exact composition of the steel used in your pistons (pretty much unknowable, especially since the particular pistons are about 20 years old)
The concentration of carbonic acid in the generated stream of CO2 (depends on the filter, the water content of the vinegar used and probably other factors as well)
The duration of exposure (that can be minimized by applying the cleaning steps outlined in your question, but consider that rinsing with water brings another set of problems, like limescale or rusting - so if I were you, I'd skip step 2 and only run it on warm, dry air to remove any moisture from the system)


Looking forward to read your experience!