It is a condition for the one performing ablution to be Muslim. Ablution is invalid from a disbeliever. This is the position of the majority: Malikis, Shafi`is, Hanbalis, and an opinion among Hanafis.  Islam is a condition for Hanafis in dry ablution (tayammum) but not in ablution, since the intention is for them a condition for dry ablution but not in ablution, though some Hanafis have stated that Islam is a condition for ablution as well.
It is a condition for the one performing ablution to be sane, and this is by agreement of the four schools of jurisprudence.
Having an intention is a condition for performing ablution, and this is the position of the majority: Malikis, Shafi`is, Hanbalis, and Zahiris.
Fourthly: Uttering the Intention
The place of the intention is the heart, and uttering it out loud is not legislated. This is the position of the Malikis, an opinion among the Hanafis, and the explicit opinion of Ahmad. It is the choice of Ibn Taymiyyah, Ibn al-Qayyim, the apparent opinion of al-Kamal ibn al-Humam, and the choice of Ibn Baz and Ibn `Uthaymin.
Fifthly: The Ending of Anything which Negates Ablution
The ending of anything which negates ablution, like vaginal bleeding, menstruation, or postnatal bleeding, is a condition for its obligation as well as validity. This is by agreement of the four schools of jurisprudence.
Sixthly: Removing what Prevents Water from Reaching the Skin
It is wajib to remove anything which prevents the water from reaching the skin of each of the respective body parts,  Examples of this include wax, fat, paste, mud, paint, fake nails, makeup and kohl if they form a layer which prevents water from reaching the skin. An example of this is nail polish, which women put on their nails for beautification. and this is by agreement of the four schools of jurisprudence.
Seventhly: Entering of the Time for One with Persistent Hadath
The time of prayer entering is not a condition for the validity of the purification of one afflicted with a persistent hadath,  Like one afflicted with urinary incontinence or flatulence. Also, the patient with a urinary catheter (a thin plastic tube inserted in the urethra to allow urination into a bag). nor is it a condition for him to perform ablution for every prayer. This is the position of the Malikis, Zahiris, and a group of the Salaf. It is also the choice of al-Shawkani and Ibn `Uthaymin.
Eighthly: That the Ablution is from Purifying (Unconditional) Water
It is a condition for ablution that it is performed with purifying water. It is not valid without it. This is the position of the majority: Malikis, Shafi`is, Hanbalis, Zahiris, a narration from Abu Hanifah, the position of Abu Yusuf, and the choice of al-Tahawi.
- Is it a condition for the water used to be permissible?
It is not a condition for the validity of ablution that the water used is permissible, and it would be valid even if performed with stolen or forcefully taken water despite it being sinful. This is the position of the majority: Hanafis, Malikis, and Shafi`is.