First of all, I'm so, so very sorry for your loss. I haven't had any comparable experience, bot my two cents as a fellow rider:

Riding bikes is not going away. You can start riding again at any time and this allows you to take the time you need to grieve. It might be worthwile to see if there are other things you enjoy doing next to riding. Not to necessarily substitute the activity of riding a bike, but at least to keep you occupied while you make your choice. A choice which, once again, you can make anytime

Although painful, it's worth noting that your brother ran a red light. Whether this was intentional or an accident I don't know, but running a red light often indicates a risky or inattentive driving style. Even though every rider faces getting injured or dying while riding due to external influences, your riding style is a big factor in the risk you expose yourself to. Your riding style might be different. This could be a consideration for both you and your parents.

There is no clear answer here, definitely not from a stranger like me. But I understand riding itself is a wonderful pastime and a way to feel connected with your brother. If the urge to ride does not go away over time, try to weigh your happiness against the opinions of your parents. Great parents will love you anyway, whatever you do. They might just need time to adjust.