Creating bitmoji's on snapchat and other apps

Pictures of all animate objects are haraam in Islam. Grave warnings have been sounded in the Mubaarak Ahaadith for those who get involved in the major sin of picture making. Nabi (sallallahu alaihi wasallam) said:

Those involved in picture-making will be subjected to the worst forms of punishment on the Day of Qiyaamah.

Nabi (sallallahu alaihi wa sallam) has cursed the one who receives interest, the one who gives interest, the tattooist, the tattooed and the picture maker. The hadeeth also explains that the angels of mercy do not enter a home in which there is a picture of an animate object. Hadhrat Abu Hurairah (radhiallahu anhu) reported that Rasulullah (sallallahu alaihi wa sallam) once said: "Jibreel (alaihis salaam) came to me and said, 'I came to you last night and was prevented from entering simply because there were images (of animate objects) at the door, and there was a decorated curtain with images on it in the house, and there was a dog present in the house. So instruct that the head of the image which is in the house be cut off so that it resembles the form of a tree, and the curtain be cut up and made into two cushions spread out on which people may tramp upon, and instruct that the dog be taken out.'" Rasulullah (sallallahu alaihi wa sallam) then did so. (Sunan Abi Dawood) Hence, a picture which does not have a head will be permissible.

Since bitmojis and anime profile pictures contain pictures of animate objects, it is not permissible for one to get involved in these things.

And Allah Ta'ala (الله تعالى) knows best.