Thank you for your question. Unfortunately, watching screens has become a common pastime for children and adults. Children do it for constant stimulation or out of addiction, and adults usually let them do it to have a break from the kids.
Please see the rulings pasted below written by Shaykh Abdurragmaan Khan about watching TV and cartoons.
The ruling of a male viewing a female
The prohibition of looking at members of the opposite sex is restricted to human beings. It is haram for an adult man to look at any part of the body of a strange, adult woman with desire. Shafi’i scholars differ on whether it is prohibited or permissible to look at the hands and face of a strange, adult woman without desire and in a situation where there is no fear of fitna.
For this purpose, fitna is defined as anything that may lead to intercourse or its preliminaries. The official view is that it is haram to look at her hands and face, even in the absence of desire and lack of fear of fitna. The unofficial view, which is the view chosen by many of our local scholars, is that it is permissible to look at the hands and face of a strange, adult woman without desire and where there is safety from fitna. [Mugni al-Muhtaj]
The ruling of a female viewing a male
Likewise, according to the official view, it is haram for an adult woman to look at the awra of a strange, adult man with or without desire. The unofficial view, which is the carried view of many of the scholars in our community, is that looking at parts other than the awra is permissible in the absence of desire and safety from fitna. [Mugni al-Muhtaj]
The viewing of non-humans
However, these rules do not apply to non-humans, whether real or imaginary (like a cartoon). It is permissible for a man to look at ,a woman’s cartoon image woman’s cartoon image provided he does so without desire. According to the Shafi’i school, looking at any object with desire, even a stone, is haram.
Summary
In short, looking at a cartoon is permissible if it is done without desire. If it is done with desire, it is impermissible.
Having said that, we have discussed the ruling on watching films, series, and television in detail in a different answer.
And Allah knows best.
Also, see the following answer, written by Ustadh Omar Popal, Watching animated television, as long as the content is lawful, is permissible.
I hope these answers give you what you are looking for, may Allah reward you for your sincerity and concern, and may He give you the best of this world and the next.
[Ustadha] Shazia Ahmad
Checked and Approved by Shaykh Faraz Rabbani
Ustadha Shazia Ahmad lived in Damascus, Syria,, for two years,, where she studied aqidah, fiqh, tajweed, Tafseer, and Arabic. She then attended the University of Texas at Austin, where she completed her Master’s in Arabic. Afterward, she moved to Amman, Jordan,, where she studied fiqh, Arabic, and other sciences. She recently moved back to Mississauga, Canada, where she lives with her family.