Was it only his parents who asked you to check his belongings? Did your friend ever ask you to do it? Or did he have any chance to tell you about bitcoin? This might be personal questions but I think before you decide how to open the wallet you should also consider what might have been the decision of your friend. If he didn’t tell anyone I doubt he wanted to leave those coins to someone, if there were any.
You may not be far from the truth, if op's friend wanted someone to know about his bitcoin wallet he would have related it either to his parents or someone else.
These questions need to be considered so as not to go against a friend's wish.
But if it's with the consent of his parents you can go ahead, they still have the right to take decision for their son but the unlocking should be done in their presence (the parents) also following the legit way of unlocking the wallet.
I am thinking if this might be one of the consequences of decentralization. Not that I think decentralization is a bad thing but in times like this, it makes me think how could one hand over his or her coins to someone without giving them explicitly the wallet before death.
At least with banks it’s all automatic. You tell them the account should be accessed by this and that but with crypto, it gets a little more complicated than that.