Sheikh Muhammad Muhammad Sâlim `Abd al-Wadûd
In the Mâlikî school of thought, there is a general legal maxim that all living organisms are pure, including their sweat, tears, saliva, and phlegm. This applies to all animals, including the dog and the pig. [Refer to: al-Kharashî’s commentary on Mukhtasar al-Khalîl]
Also, the Malikî school regards the condition of washing the saliva of the dog with dirt to be weak from a hadîth standpoint. The various hadîth narrations that contain this instruction are inconsistent and contradictory in their wording. The Malikî scholars argue that according to the methodology of hadîth criticism, when various narrations of a hadîth provide inconsistent and contrary wordings, the hadîth cannot be acted upon. Consequently, the Mâlikî school of thought does not require washing off dog saliva with dirt.
On the basis of what we have explained, it is permissible for you to adopt the Malikî ruling on this matter in order to alleviate the hardship that you are facing.
And Allah knows best.
Source: Islam Today