In Islam, the general principle regarding permissible entertainment is that it is allowed so long as it does not involve anything haram, does not distract one from obligations, and does not lead to heedlessness or sinful behavior. There is no requirement in Islam to avoid all forms of permissible entertainment, nor is there an obligation to participate in it.

At the same time, Islam places great emphasis on maintaining family ties, kindness, and good companionship within the household. Allah تعالى says: “And live with them in kindness.” While this verse is specifically about marital conduct, scholars note that its spirit applies broadly to family relationships—namely, interacting with gentleness, consideration, and emotional presence.

If you personally do not enjoy cartoons and do not watch them out of habit, there is no religious blame on you for choosing not to participate. Avoiding something permissible out of personal preference or a desire to protect one’s time and heart is allowed and can even be praiseworthy if it helps you stay focused and spiritually grounded.

However, occasionally sitting with your family during such moments—without actively engaging or endorsing anything impermissible—can be an act of good character and family bonding, especially if your intention is to maintain warmth, harmony, and connection. The Prophet ﷺ said: “The best of you are the best to their families.” This includes being emotionally present and considerate of shared family moments, even when they are not your personal preference.

What is important is balance and intention. You are not required to force yourself to watch something you dislike, nor should you feel guilty for stepping away politely. At the same time, if joining them occasionally does not harm your heart, waste excessive time, or expose you to haram content, then doing so out of compassion is permissible and can be rewarded based on your intention.

If you feel frequent inner conflict, it may help to gently communicate your preferences to your family, while also reassuring them of your care and presence in other shared activities. Islam does not demand uniform habits within a family, but it does encourage mutual understanding and mercy.

Summary ruling:
You are not obligated to watch cartoons or entertainment you do not enjoy, but occasionally joining family out of kindness and connection is permissible and can be rewarding if done with good intentions and without harm to your values.