The take-home and parent policies are important in ensuring student safety while off-campus. It is important to remember that parents can manage their kid’s filtering only after they activate their parent account. If the account is not activated, then school-determined policies apply.

This article will help you understand how the two interact with each other.

Only take-home policy: The rules determined by the admin for the take-home policy would apply, including category restrictions and allow & block lists.
Only parent policy: Depending upon the control levels determined by the admin, the parent can manage the categories for their kid. The parent can create the Allow and Block lists and will apply to the kid’s activity at home.
Take-home policy + parent policy: Similar to #2, depending upon the control levels the parents would have access to determining which categories and settings they can edit. If you want to give your parents greater flexibility in determining which categories are open or blocked for their kids, consider configuring less restrictive controls for them. At the same time, the Allow& Deny lists created by the parent as part of the parent policy would take precedence over the take-home policy lists.
No take-home policy + parent policy: In this case, the parent would be able to control their kid’s filtering and allow/block lists as per their control levels. However, if the parent has not activated their parent account, then the kid would be filtered as per the policy assigned to their OU, along with the allow/block lists of that policy. If no policy is assigned, the default policy will be applied.

What to expect when using parent policy and Take-home policy together?