I think the source is the bigger problem. If they take the water from sources which are already scarce, the impact will be harsh. There probably wouldn't be any complaints if they would use sewerage or saltwater from the ocean.
> Also, it's pretty easy to recycle the data center water, since it just has to cool
Cooling and returning the water is not always that simple. I don't know specifically about datacentres, but I know about wasting clean water in other areas, cooling in power plants, industry, etc. and there it can have a significant impact on the cycle. At the end it's a resource which is used at least temporary, which has impact on the whole system.