Well I was 15 when I first got into Green Day and since I made it my occupation to get all of their albums and my family could not keep up with which ones I already had and which I didn't, they all took to getting me "similar bands" albums for every birthday, Christmas or special occasion. I could just imagine them walking into a record store and asking the staff for their recommendation of bands a 15 year old girl into Green Day might enjoy. This resulted in my getting a lot of Blink 182, Simple Plan, My Chemical Romance, Good Charlotte, and other bands I cannot remember, and me hating them all because I just felt so patronized I have since revisited a few of them and still don't like them (although I have really grown to appreciate MCR's Black Parade since my friend made me listen to it to get me to go with him to their show next year, but I am still firmly not into the rest of their stuff).
At that time instead I turned to discovery older punk and older rock on my own, and I did become a huge fan of those. But I do wonder if the situation had been reversed, and my auntie had given me a The Who album for Christmas when I was 15 instead of Good Charlotte, if I'd be a huge fan of Good Charlotte right now
Anyways, very verbose answer, sorry.
I really like Radiohead, but I would not think they are at all similar to Green Day