Is it permissible to make ablution without having to perform istinjaa and wash one’s private parts?

Washing front and back openings (Istinjaa`) is not a condition for the validity of ablution because it is done to remove Najasa (impurity), thus if there is no Najasah, there is no need for that, and then it is permissible to make ablution without answering the call of nature.
However, prayer is invalidated if there is Najasah on the anus, or the front opening, so it (Najasah) must be removed for the prayer to become valid, and not the ablution.