The objection correctly asks why a sincere prayer should depend on washing. The answer is that wudu is not based on the idea that sweat or dust makes a person morally impure; it is a divinely appointed act of preparation, with practical and spiritual wisdom, and it is not required before every prayer if one's wudu remains valid.
What the objection gets right
A person may have clean intentions, be deeply repentant, and still have dusty feet or sweaty hands. Those physical conditions do not make anyone sinful or spiritually worthless. Nor does Islam teach that God is deceived by outward washing while ignoring the heart. A prayer performed without the required purification, however, is not valid as the formal act of prayer, just as fasting outside its appointed time is not the fast God prescribed.
The objection also fairly observes that hygiene alone cannot explain wudu. Clean water is not always available, and someone can be physically clean while still being required to perform wudu. So the rule is ritual, not merely sanitary.
What the Quran actually gives as the purpose
O believers, when you rise to pray, wash your faces and your hands up to the elbows, wipe your heads, and wash your feet to the ankles. If you are in a state of major impurity, then purify yourselves. But if you are ill, on a journey, or unable to find water, then perform tayammum with clean earth, wiping your faces and hands with it. Allah does not intend to inconvenience you, but to purify you and complete His favour to you, so that you may be grateful.
Quran 5:6
The verse itself gives more than one dimension: purification, gratitude, and ease. Wudu makes prayer a deliberate transition from ordinary activity to standing before God. It disciplines the body, gathers the attention, and repeatedly reminds a Muslim that worship is received on God's terms rather than according to personal preference. Washing the limbs associated with daily action can also symbolize presenting one's actions, perception, speech, and movement to God.
Yet these are wisdoms, not the entire legal reason. A command from the all-wise God does not become unreasonable merely because its full rationale cannot be reduced to one measurable benefit. Many acts of worship contain meanings we can understand without being exhausted by them.
Why tayammum matters
Tayammum is especially revealing. When water is unavailable or harmful, clean earth replaces it. This shows that wudu was never simply a demand for hygiene, nor a claim that dirty hands make prayer spiritually worthless. It is a form of ritual readiness, while the concession shows that God does not seek pointless hardship.
Therefore, the objection establishes that wudu is not explained by sanitation alone. It does not establish that the rule is irrational or that sincerity can replace a condition God attached to prayer. In Islam, sincere prayer includes sincere submission: the heart is directed to God, and the body follows the form He prescribed.