Firstly, I assume that you reside in a jurisdiction where converting from your original religion to Buddhism and the practice of Buddhism are not illegal.
I suggest that you can explain the following to your parents, assuming that it is possible to reason with them:
I understand and respect your beliefs and your practice of religion X. This religion X teaches one to have morality, respect, kindness and compassion for your fellow man. The founder of this religion also displayed these values. (cite examples here)
I would like to announce to you that I do not belong to religion X any more, although I still greatly respect it and its founder. I have now accepted Buddhism, as my religion and my way of life, by taking refuge in the Buddha, his teachings and his community of disciples, as well as by undertaking the training of the Five Precepts of Buddhism.
The Buddha also displayed the same values of morality, respect, kindness and compassion, that the founder of religion X did, and he taught his followers to practise these values. (Cite examples from the Buddha's life that parallel the life of the founder of religion X)
The Five Precepts of Buddhism are not very different from the Ten Commandments (or some other equivalent teaching of religion X). It teaches me not to kill, not to steal, not to commit adultery, not to speak the untruth, and not to consume intoxicating substances. The Buddha is not God and Buddhists are not required to make idols of the Buddha, or worship him. Taking refuge in the Buddha simply means that one accepts the Buddha as his teacher, and has faith in his teachings.
The Buddha was a normal man, who became an enlightened teacher, who guided his followers away from living an immoral life that leads to suffering, just as the founder of religion X did.
The Buddha also taught his followers to respect and cherish their parents. He taught that it's very difficult for children to repay the love and kindness shown by parents towards their children.
I want you to understand that your insulting and belittling of Buddhism or the Buddha will not change my mind. I am now and for the foreseeable future, a committed practising Buddhist.
The founder of religion X did not prevent or hinder people from following other religions. The Buddha too did not prevent or hinder people from following other religions.The founder of religion X did not force others to practise the religion that he brought. The Buddha too did not force others to practise his teachings.
Similarly, I will not force you to practise my religion, and I ask you not to force me to practice your religion. I will not insult or belittle your religion, and I ask you not to insult or belittle Buddhism.
Even if you insult or belittle my religion, the Buddha taught me to show metta (loving kindness) towards you. By metta, I mean I would always wish you to be happy and free from suffering. (Cite similar examples from the life of the founder of religion X, if possible)