What is the ruling regarding someone afflicted with impurity who is unable to wash it due to insufficient water or fear of water stains remaining on clothes and causing embarrassment for the traveler?

Purifying oneself from impurities takes precedence over performing ablution (Wudu') if the water is insufficient for both, because Wudu' has an alternative, which is Tayammum (dry ablution), unlike the removal of impurities. If no water remains after removing the impurity, one should perform Tayammum, and their Tayammum is not valid until after the impurity has been washed away. If there is enough water to remove the impurity, then seeing wetness on clothes is not an excuse to abandon purification.