Judging you for something you haven't done, but look like you're in position to despite not intending to? Paul (that is, an elder your parents should listen to) would have this to say about that:
You, therefore, have no excuse, you who pass judgment on someone else, for at whatever point you judge another, you are condemning yourself, because you who pass judgment do the same things. Now we know that God’s judgment against those who do such things is based on truth. So when you, a mere human being, pass judgment on them and yet do the same things, do you think you will escape God’s judgment? Or do you show contempt for the riches of his kindness, forbearance and patience, not realizing that God’s kindness is intended to lead you to repentance?
Don't your parents have any friends married to other people? Tell them that it's arrogant for them to presume your motives when the Lord knows that you're not going to do anything untoward. The Bible specifically encourages love without passion, because even a married couple getting to know one another is in that moment closer to worldly matters than to God. And no, at least based on my cursory search, the Bible does not tell anyone to "not allow themself evil appearances". On the contrary, several quotes (e.g. John 7:14-24; 2 Corinthians 10:7-18; Colossians 2:16-23) specifically tell not to care about what your actions look like in this life, as long as their intent is pure.
Disclaimer: I don't consider myself a Christian, and haven't read the whole Bible. I believe there is some useful if outdated wisdom in it, but that it should be taken allegorically and that nobody should follow it blindly.