All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
First of all, we congratulate you for the blessing of embracing Islam; this is indeed one of the greatest blessings, which requires a person to be thankful and grateful to Allah.
The best way of being grateful is to seek beneficial knowledge, perform good deeds, keep company with righteous women, attend gatherings of goodness, and do everything that would help you remain steadfast on the true religion until you meet your Lord, Who will be pleased with you and will make you inherit Paradise, Allah willing.
Islam mandates being kind and dutiful to the parents even if they are non-Muslims. Allah says (what means): {But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them but accompany them in [this] world with appropriate kindness and follow the way of those who turn back to Me [in repentance]. Then to Me will be your return, and I will inform you about what you used to do. .} [Quran 31:15]
It is clear from this verse that being kind and dutiful to them does not mean obeying them in what is not pleasing to Allah Almighty; obedience is only in what is permissible, as in the hadeeth which was narrated by ‘Ali, may Allah be pleased with him, and in which he reported that he heard the Prophet say, “There is no obedience [to anyone] in disobeying Allah; indeed, obedience is only in what is permissible.” [Al-Bukhaari and Muslim]
The hijaab, which is what covers the entire body with the exception of the face and hands is an obligation on the Muslim woman according to the consensus of the scholars, so the parents are not obeyed in regard to removing the hijaab; please refer to fatwa 90199.
Therefore, in principle, you must wear the hijaab when leaving the house, but if there is a real fear of being harmed because of wearing the hijaab, then you should stay at home and not go out except for a necessity. If you go out for a necessity, then you must not reveal of your body except the extent that you hope would repel harm, because necessity is weighed according to its proper value.
If the necessity ceases to exist and you feel safe, then it is an obligation to go back to the principle state, which is to wear the proper hijaab according to the Shariah.
In conclusion, we would like to draw your attention to a very important matter, which is that the best way of being kind and dutiful to your parents is to endeavor to guide them to Islam and encourage them to embrace it, especially through good conduct with them and other matters that show the good traits of this religion and which may be a reason for softening their hearts to Islam.
The Prophet said to ‘Ali, may Allah be pleased with him, "I swear by Allah! If Allah guides one single man (to Islam) by your efforts, that will be better for you than possessing the red camels (a very expensive breed of camels which was considered to be the most valuable property in the sight of the Arabs)." [Al-Bukhaari and Muslim]
For more benefit, please refer to fatwa 260962.
Allah knows best.