The only two concerns are (1) battery acid and (2) hydrogen gas.
Hydrogen gas is explosive, but to explode you need 4% of it in air. This means that in a 30 square meter, 2.6 meters high room, you need 0.04*78 = 3.12 cubic meters of it. Hydrogen density is 0.08375 kg/m3, so you need 0.26 kg of hydrogen.
Water is H2O, so to cause an explosion, you need
(16+2*1.008)/(2*1.008) * 0.26 kg = 2.32 kg of water to be completely separated to hydrogen and oxygen.
Car battery is 7 liters in size approximately. However, not all of that is water-acid mixture. If we assume 25% of the size is battery casing, and of the rest, 50% is lead plates and rest is water-acid mixture, we have
0.75 * 0.5 * 7 l = 2.63 l of water-acid mixture.
Battery acid is 37% sulfuric acid, rest water. So a quick approximation is that it's 2.63 l * (1 - 0.37) = 1.66 l of water.
I don't think there's enough water to cause an explosion hazard if charging a battery indoors, even if all the water was turned into hydrogen so quickly that your ventilation system can't clear away the hydrogen (which would require all of the water being electrolysed in way less than an hour).
The main hazard is that if the charger you have is faulty (or too simple, not microprocessor controlled), theoretically it's possible that the bubbles splash acid around, and if the vents release hydrogen gas, some small amount of acid could get away from the battery. This won't happen with an AGM battery. But with a flooded battery it's theoretically possible that you get battery acid on the floor or wherever you happen to have the battery. If you notice it, the solution is simple: use sodium bicarbonate water solution to neutralize it. If you don't notice it, theoretically it's possible it could cause acid burns to your fingers if you touch it.
The best bet is to charge your battery at the car. But if you for some reason can't have electricity there, bringing it indoors is not a criminal offense. It may be useful to charge it in bathroom, so if any acids leak you can dilute them to practically no acid left simply using water -- maybe adding some sodium bicarbonate there to neutralize it if you want to do a perfect job.
Also, if charging a battery, do something to prevent localized hydrogen explosions (so that the entire area doesn't have explosive concentration but a small amount of air near the battery has an explosive concentration): remove the AC side of the charger first, and only then remove the DC side to prevent sparks, or alternately if charging on the car connect the charger negative lead very far away from the battery to some metallic grounded object -- or both.