Is it permissible for a Muslim to pray Fajr with tayammum, without ghusl from janabah, if he wakes up in a state of impurity, fearing he would disturb his neighbors if he were to perform ghusl?

The excuses that permit tayammum are an illness that prevents ritual purity, or the absence of water. Disturbing neighbors is not an excuse that permits tayammum. Rather, one must ask them for water unless one is certain that they will not provide it. If one performs tayammum without asking, despite the presence of water, one must repeat the prayer according to their state of belief, doubt, or mere assumption that they would be given water.