Can you use coffee or tea instead of water in a sourdough starter?
Well no-one will shoot you if you do. But there are obvious downsides: yeast is killed at 55C to 60C, and slightly higher temperature will kill many lactic acid bacteria. So unless you cool the tea or coffee you'll simply kill the starter. Moreover caffeine has an inhibiting effect on yeast growth (see Figure 5), so your feeding regime will be less effective. 

If you want to make tea or coffee flavoured bread, I would instead add instant espresso powder to the dough, or replace some of the water with (cold) strong tea. Given the article above, it might also be a good idea to use extra starter/yeast.