My master bath exhaust fan has two switches, one on either end of the bathroom. Both are standard on/off flip switches.

Is there a way for me to replace one of the two switches with a timer, similar to the one shown below, and still have the other binary switch continue to function?

A quick Google suggest no, but I figured I'd check here.

It appears from that quick Google that my options may be:
A) Disconnect the secondary switch and just use the timer
B) Keep the second switch wired, with the understanding that it can only act as a cutoff (i.e. it has to be "on" in order to allow the timer to function, but cannot activate the fan itself)
C) Replace both switches with a pair of fancier specialized coordinating switches/timers at $30-$50 each.
D) Leave it as-is and just continue to live without a timer.

Is there another option here?

Yes...I think.

I have something similar. The toggle switch for the bathroom fan/light is on the wall going into my bathroom. Inside the bathroom I have a similar timer switch, but it operates the heater portion of the fan. I assume it could be wired to a non-heating fan.

B this is what we did with a motion detection switch in the mud room, the other switch kills the circuit, you just leave it in the on position and the motion (in your case timer) controls.

If your requirement is to always have the fan run for a predetermined period, e.g. for 15 minutes after a shower, a timer connected in series with the fan rather than either switch might be a better option.

No you've named them all.

You could do a motion sensor, but that would leave it turning on whenever you walk in, not just when you shower. I wouldn't have a problem with that set up, but I leave my bathroom fan on 24/7 anyways. Plus if falls under option C) will cost about $30 for the switch.

Here's you other option C) - probably around $60:

3 way countdown timer.

Companion switch.