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There are a number of things that are unclear.  You talk about the red and IR phases of the light sensor signal being demultiplexed into separate red and IR signals, but there is no evidence of this in what you show.  If this is happening at all, the crucial information of what each filter is driven with when not receiving the photosensor output is missing.

I took a quick look at the document you linked to.  Keep in mind this was written by a semiconductor company trying to sell parts.  It should by no means be taken as some sort of best practice for pulse-ox meters.  I expect they got something to work in the lab, but that's all.  Getting it to work is at least something, but it's not proof of great design.  Remember, they're trying to sell parts, and aren't on the hook for whatever you might design from this document.

There are a few hints that this is a less than meticulous design.  Attention to detail is clearly lacking, which makes the whole design rather suspect.  For example, in the bottom filter, C33 and R79 are described as a high pass filter with 800 mHz rolloff.  That's true when considered in isolation.  However, since the output is loaded by R81, C33 is really working against 41 kΩ, and the rolloff frequency is really 1.2 Hz.  This is pretty basic stuff.  Even the intern should have caught that one.

Even worse, in the top filter, all three parts are included in the box, still labeled with 800 mHz.  That's just plain wrong.

Also notice how no care was taken to draw the two identical filters identically.  Whoever drew this never heard of copy and paste?  Lines overlap text in a few places.  What's with all those dots on one side of each capacitor and resistor?  Why are there two junction dots on either side of C33?  C34 doesn't have them.

This isn't some quick sketch in someone's private notebook.  This is in a formal publication by a large company.  The whole drawing exudes a <i>"Eh, who cares"</i> attitude.  This is who you want to take advice from for designing a medical product!!?  If this is how little they care when trying to make a good impression, imagine how sloppy they are about things you can't see.

To actually answer your question, we can't know why they used two separate filters unless they explicitly say so.  However, here is a guess.

The two filters have long settling times.  When one filter is driven with the light sensor signal, the drive to the other is switched to high impedance.  That together with the large input capacitors (C31 and C32) works like a sample and hold.  Therefore each filter can settle over times longer than the red/IR switching time.  Again, this is just a guess.

The outputs of the two filters being multiplexed and then driving a single A/D is not surprising.  Microcontrollers usually come with multiple analog inputs per individual A/D, and an analog mux to select one at a time.  Sequencing thru the various analog inputs over successive A/D readings is a normal thing to do.  Note that the upper frequency of interest is apparently 6 Hz.  Using half the A/D sampling rate per signal shouldn't be any problem.

The real question I have when looking at this circuit is why more isn't done in the firmware instead of in analog hardware.  With the meaningful signal having only 6 Hz bandwidth, this really seems like a no-brainer.  Even low end micros could easily sample each signal at around 1 kHz, demultiplex the red/IR in firmware, then low pass filter and decimate each stream before applying further processing.  You do need some analog filtering to avoid aliasing, and reduce the noise enough so that it doesn't cause clipping before it is removed, but that doesn't require much complexity.