Pretty much whenever you move, the water will taste different. Maybe it'll be harder, maybe softer, maybe it'll have been purified with a different process or different chemicals. Chances are, you may not like it to start with, and may even have to get a different kind of tea (oh the horror!). However, this question isn't about that...
There's a fair bit of the world where locals can drink the water without issue, but visiting tourists are generally advised to drink bottled water to avoid Delhi Belly and the like.
If you find yourself moving to such a place, drinking bottled water might be fine at first, but is unlikely to work long term. At some point, you'll come across ice cubes made with local water, drinks made with local water, fruit or salad washed with local water, or something like that.
Knowing this, and knowing the initial risks of GI problems, how do you go about acclimatising to the local water in a situation like that?