Yes, it would be entirely appropriate and considerate to include a message like "Gifts are appreciated but not mandatory" on a birthday invitation. By doing so, you are showing sensitivity to the financial situations of the families of the invited children. This approach helps ensure that every child feels welcome and comfortable attending the birthday celebration, regardless of their ability to bring a gift.
Including such a message on the invitation can also help shift the focus away from material gifts and emphasize the joy of coming together to celebrate the birthday child's special day. It allows guests to focus on the fun and shared experiences rather than feeling obligated to bring a present.
Additionally, some families might have their own cultural or personal reasons for not giving gifts, and stating that gifts are not mandatory acknowledges and respects their preferences as well.
Remember that the main goal of a birthday party is to celebrate and enjoy the company of friends and loved ones. By being inclusive and understanding of different circumstances, you can create a warm and welcoming environment for all attendees.