Gas fireplaces are safe, convenient, and very popular today.
Because of the sealed combustion system and the coaxial venting system used in gas fireplaces, the likelihood of a unit causing issues with most common allergies is remote.
Wood-burning equipment differs because of the inherent smoke and the possibility of a moldy wood supply. But with gas, since the fireplace's glass is gasketed and the venting system is sealed, no room air interacts with the combustion.
So, no smoke or fumes in the house.
The space below the logs and fire is readily accessible and should be kept clean of dust and pet hair. Otherwise, the blower fan will circulate warm air along with the dust and pet hair back into your living room. Since some people with allergies might react to the odors of this warm air and dust, inspecting and cleaning this area regularly is essential.