Is it permissible to wear gloves during the state of Ihram, especially during Tawaf and Sa'i, to avoid touching men and nullifying Wudu?

It is not permissible for a pilgrim (muhrim), whether male or female, to wear gloves, due to the Prophet's (peace be upon him) saying: "The female pilgrim (muhrimah) should not wear a niqab nor gloves."

As for touching women during Tawaf and Sa'i, touching a non-mahram woman is forbidden. A man should be cautious and keep away from areas where women are. If he touches a woman unintentionally, there is no sin upon him, for Allah Almighty says: "And there is no blame upon you for that in which you have erred, but [only for] what your hearts intended."

It has been previously stated that touching a woman does not invalidate ablution (wudu'). As Sheikh Ibn Baz (may Allah have mercy on him) mentioned, a man's touching a woman's body during Tawaf or in a crowded situation does not harm his Tawaf or his ablution, according to the more correct of the two scholarly opinions. The stronger opinion is that ablution is not invalidated by touching a woman at all, because the default is the validity of ablution.