The opinion that it is permissible [to perform ṭawāf without wuḍū’] is stronger, but a person should not do this unless there is a need for it, such as breaking the wuḍū’ during times of congestion – then the need for this opinion is required – because a person is unable to leave and perform wuḍū’. Or perhaps a person has companions, and if he leaves, he will delay them. But if a person is not busied or under any preventative measures, then they should not perform ṭawāf except while being in the state of having wuḍū’ – so as to avoid scholarly disagreement. “Leave what causes you doubt for that which does not cause you doubt”.
And this opinion that we stated, it was the choice [opinion] of Shaykh al-Islām, Ibn Taymiyyah, may Allāh have mercy upon him.
Sunnah Studies 