as long as it is cured properly, and allowed to out-gas for long enough, then it can be made safe - some resins take longer than others, and some of them are never safe used in this way; not all resins are equal, some are safe, some are not...even the safe ones need appropriate time to cure and out-gas to become safeSo how come ponds that are fibre glassed & under water 24/7 dont kill all the fish?
Has the background been sealed do you know. There are several companies that make fibre glass backgrounds for reptiles & aquarium use. Possibly contact one & see what they say. Might be able to tell you what to use to seal yours if it hasn't been already.
Can you not put the viv out side to air at all?