What is the advice for someone who does not celebrate the Mawlid (Prophet's Birthday), while their family does and accuses them of not loving the Prophet or of having a new understanding of Islam?

Firstly, you have done well by abandoning the celebration of mawlid (Prophet's birthday) which is an innovation (bid’ah). Do not pay attention to those who criticize your uprightness, for even the prophets were mocked before.

Secondly, my advice to you is to avoid arguing with those who will not benefit, and to select the intelligent among them to explain the reality of mawlid, its ruling, and its corrupt nature, through the following points: 1. Ask about who was Muslim earlier: Was it those who celebrated the mawlid or those who did not? The Companions and their followers did not celebrate it; rather, its celebration appeared much later. 2. Ask about who loved the Prophet more: Was it the Companions or those who came later? The Companions loved the Prophet more, and they did not celebrate his birthday. 3. Explain that the meaning of loving the Prophet is to follow him, as Judge Iyad said: "Whoever loves something prefers it, and the first of these is: emulating him, acting upon his Sunnah, and following his sayings and actions." 4. Explain that the Prophet's birth date is not definitively established, while his death date on the twelfth of Rabi' al-Awwal is established. This is the day the innovators celebrate, and the Fatimids invented this innovation to show joy at his death and to distort the meaning of love.

Thirdly, be patient in your adherence to the Prophet's Sunnah, and do not be deceived by the large number of those who differ. Be keen on seeking knowledge and benefiting people, and be gentle in your disapproval towards your family, showing them the effect of adherence in your conduct.