The Tannins will do NOTHING to your want or fish. It just makes water look a bit yellow. Some say the fish enjoy it. I bet some do. After a few months you will see little to no tannins in your tank.
Nothing is far too strong of a word, because tannins do have some useful functions. As mentioned, their effect on pH is going to be pretty tiny. Most water will have enough buffering that the weak acidity of the tannins will have no significant on pH per our highly inaccurate tests (you would need lab-grade equipment to detect the tiny change that will happen).
But, tannins do perform some very nice functions for your fish and if you have plants, the plants, too. For the fish, tannins are very good about locking up heavy metals and binding to them. When bound up, they are significantly less toxic than they are unbound. So, your fish will have this extra layer of protection from heavy metals. This is important because depending on the metal, they may not may not be regulated by your water company. For example, the amount of copper in our water can be well above toxic levels for fish before they are even tasted by humans (and the level at which they can be tasted is well below levels where they start to harm humans). This is of course, species specific, but many species have a low tolerance of copper. If there are tannins, they will bind up to the metals, and help protect the fish.
Also, some fish do seem to be triggered to spawn when tannins are present.
Finally, if you have plants, micronutrients and metals that plants do need a tiny amount of, are much easier to absorb when they are in their bound up state. So, tannins help your plants stay healthy by making it easier for them to take up their nutrients. It is kind of a neat cycle in that dead and dying plant matter releases tannins that take up micronutrients making it easier for growing plants to get their nutrients.