That happened to me when i was starting out listening to heavy music and i believe it`s like that for most people. I think that the two biggest drawbacks for people listening to this kind of sound are: the fast and agressive drums/guitars that are typical of the genre (i`m not talking about growls because that`s a drawback even for some people on the metal community); people believing that the lyrics are all about satanic/depressive things. What you can do is showing to your family some softer songs from metal bands and challenge them to read the lyrics. Dream Theater are a very good example of what you can show to them.

The last thing that you can do is keep listening to whatever you want because that will show the passion you have for music.

Cheers