If the chemicals in our food are that bad, how come the regulators and governments allow this?

Governments and regulators ideally should not be allowing this. But they do because of many other considerations. 

Firstly, the companies who manufacture food products with chemical additives are themselves asked to show data to prove that the food they are manufacturing is safe for consumers to consume. The Governments do not have the resources to conduct extensive research on the impact of these chemicals on human health. Asking the manufacturer is like asking a party with vested interest. It makes sense for them to say that their product is safe. 

Secondly, the impact of chemicals on health is not analyzed over the long term. The studies are mostly short-term. So the regulators come up with the concept of MRL (Maximum Residue Limit) for each chemical in any food. The MRL is determined based on short-term studies. But in reality, we consume these foods day in and day out for years together. The very fact that MRL is specified shows that the chemical is dangerous. Just that we are accepting it because it is in small quantities. Further, the combined effect is also not studied. We consume many food products on any day. Each food product may contain different types of chemicals. How do they interact with each other, no one knows! Have we not heard our doctors tell us not to have certain medicines along with certain others? So the testing is inadequate, and to be fair, cannot be done for all the combinations of the chemicals we may consume on any given day. And that could be dangerous in a totally different way. 

Thirdly, the governments are more inclined in a developing country like ours to approve products in the "larger interest" of industry, employment generation and tax revenues. Finally, should it not also be our responsibility to ensure that what we eat is safe? Why rely on the government entirely?