For Acoustic Guitar
You probably can do a reasonable job using a keyboard amp with an acoustic guitar. You may need a pre-amp pedal (or similar) to boost the signal from your guitar in order to use it with a keyboard amp, and you may want to adjust the equalization when switching between guitar and keys, but other than that, acoustic guitars often sound good through keyboard amps.
Going the other way, some dedicated acoustic amps will have a less flat response, and thus might affect how the extremes of the keys sound. In addition, there is some risk that lower bass sounds may overextend the speaker, damaging the amplifier. For this reason, I'd avoid using a guitar amp for keys (or bass guitar for that matter), unless you can confirm that a given guitar amp will be robust against bass notes from your keys.
For Electric Guitar
Optimally, yes, you want separate amp setups for the keys and guitars.
user20352's answer correctly indicates that guitar amps (for electric guitars) typically significantly color (modify) the guitar's sound. Without this coloration, electric guitars sound thin. Since keyboard amps don't provide this functionality, you need to add external effects into the signal chain to provide the color, prior to (effectively uncolored) amplification by a keyboard amp.
One option where you would not need to by two separate amps is to get a full-range high fidelity keyboard amp, and use an external effect that includes amp simulation in the input chain for the electric guitar sound. Thus you'll still need extra equipment in order to get full guitar tones.
Many multi-effects units, Line-6 pods, Vox tone lab, Axe-FX etc. have these kinds of amp simulation capabilities, and can be used only with a power amp (which is what most keyboard amps behave like). In addition there is at least one manufacturer of dedicated pedals for this purpose, Tech21 (Sansamp and related pedals). Finally, one may find that an appropriate combination of guitar pedals, possibly including overdrives/distortion, may provide the sounds you want, even without any any additional coloration from the amp itself.
All in all though, this is a compromise solution, and with it, you may not be able to achieve your desired guitar tones, esp. if amplifier distortion is an essential ingredient.
Running keys through electric guitar amp
I'm pretty sure that going the other way, running keys through a guitar amp, has been done -- mostly back in the 60s, but the coloration imposed by the guitar amp limits how well you can use the full range of the keys. This might be a feasible approach if you were only going for a limited range of vintage sounds with your synthesizer. Again, running keys through a guitar amp, esp. loud bass notes, can overdrive the speaker and cause permanent damage.