The quick answer: I don't think neem is safe to use in the restricted, closed environment of a vivarium or paludarium.
The details: Unfortunately neem is not safe for fish and other aquatic organisms. That doesn't mean you can't use it if fish or frogs are present. It depends on the specific use.
Using it in a vivarium/paludarium would not be safe in my opinion. I don't know what exactly you want to do, so maybe read through the details below and draw your own conclusions.
Neem extracts are not safe for fish. These studies have more information about the exact concentrations that are harmful. (Note that the neem extracts were added directly to the water.)
Toxicity of neem pesticides on a fresh water loach...: "The fish under toxicity stress suffered several abnormalities such as erratic and rapid movement, body imbalance and surface floating responding proportionately to the increase in concentrations of the toxicant biopesticides."
Acute lethal and sublethal effects of neem leaf extract on the neotropical freshwater fish...: "Fish exposed to all neem extract concentrations exhibited damaged gill and kidney tissue. These results indicate that although neem extract is less toxic to P. lineatus than other synthetic insecticides used in fish-farming it does cause functional and morphological changes in this fish species."
Other studies looked at a range of aquatic organisms, such as mosquito larvae and tadpoles. In some studies the neem compounds were toxic to all tested species, others reported that some organisms were unaffected.
There have also been some studies looking at the environmental effect of agricultural/forestry use of neem sprays on neighbouring water bodies. Here is one that concludes that it does not pose any problems:
Ecological risk assessment of neem-based pesticides: "The aquatic risk assessment process showed that the risk values of tested pesticides did not exceed the criteria, and therefore, no ecological hazard is likely to result from their use."
Ok, have I confused you enough?
What I concluded after reading through a couple of dozen of those studies is this:
Don't use neem in water. Use on land is fine.
The active compounds in neem are not stable in the environment, not at all. So unless you spray directly into a body of water, you should be fine. Agricultural use is fine. Take care near small, shallow and standing bodies of water.
Use in vivariums/paludariums? I would not risk it. No matter how you apply the neem product, chances are it will end up in the water.
Longterm effects of Neem on fish by: Anonymous
Some of the comments indicate that Neem is harmful to fish. I know that Pyrethrins, though natural and less toxic to vertebrates, are deadly to fish when they wash from land and/or run-off to rivers, ponds, oceans etc. Is Neem in this category, or does it break down more quickly than pyrethrins?
Neem breaks down quickly by: Birgit
Neem breaks down very quickly when in contact with moisture and under UV light. There is not as much danger from it being washed into streams, unless it happens straight away.
It shouldn't be applied right near water where it could enter the water immediately, or where overspray may hit the water etc., and I certainly would not recommend using it in a confined, moist environment like a vivarium. But during normal use outside there is nothing to worry about.
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Neem should not be taken by anyone who is pregnant or trying to conceive. Neem contains compounds similar to those in aspirin and must never be used to treat children with fevers. It should not be taken by people with known allergies to aspirin and aspirin like substances. Neem oil should not be taken internally.