Being is the same room is one thing ... using the same play area, without cleaning it throughly between each of them
every time one comes out to play, is something else.
One dropping of poop with Guardia can spread it from one animal to another.
Washing your hands between holding them is good, but what about the clothes you have on ... your clothing could spread some things as easily as your hands can.
Gerbils are usually pretty healthy, so are chins, but if one gets sick, regardless of what it is, I would not be surprised if they did not both get sick.
CA Chins, a chinchilla research center, is finding out (as we all are) that chinchillas can get/contract/pick-up most any disease or illness from anyone or any animal. What we once thought they could not get, with all the new exposures to so much more, as pets, they have found out, a chin can usually catch it.
Any new animal should have a vet check and a reasonable quarantine time, just for safety's sake. How much time? Depends on what you are comfortable with. With some illnesses, a chin will show signs of it in less than 24 hours (feline distemper - spread by contact ), then there is at least one thing I know of (stomach warts often found in goats - is viral and air born), that may not show up for 9 weeks to 9 months. Both could kill an entire herd.
You really don't know ... you have to make those decisions ... but keep in mind ... it's like having a child that is allergic to bees ... would you deny that child the pleasures of the out-of-doors for the rest of it's life for fear a bee would sting them? Or would you allow them to play (but not in the flower garden) and keep meds near by for them?
It's just one of those things you each have to decide for yourself.
Jo Ann