Is it permissible for Muslims in Karnataka, India, to follow Saudi Arabia in determining the beginning and end of Ramadan, given their disagreement with the state's determination which does not rely on moon sighting, and what should one do if they fasted with them?

A Muslim residing in a country that relies on legitimate رؤية (sighting) must conform to their fasting and breaking of the fast. However, if they are in a non-Muslim country or a country that does not observe legitimate sighting, they should follow the closest country that seeks to sight the crescent moon, or fast with a country whose sighting is reliable, such as the lands of the Two Holy Mosques. If India fasts later than the countries that seek to sight the crescent moon, then whoever fasted with them must break their fast with the country that sighted the crescent moon and make up one day in place of the first day of Ramadan.