I don't think respect is the right word to use here. If Dream Theater wouldn't exist without The Beatles, fine. Cool, thanks Paul and crew for making music that inspired a future band that would end up being my favorite. Oh, you know which band inspired Jon Schaffer of Iced Earth to play guitar for a living? KISS. Do I like them? NOPE. Not even a little bit. Well, that's not true. Iced Earth has a good cover of Creatures of the Night. I'm not going to fault myself or place the blame on myself for not liking something. Again, I don't think respect is the right word to use. I don't ever say I respect DT or Iced Earth even though I love their music and think the musicians are pretty cool and don't afraid of anything.
But no one said anything about LIKING. I could care less about LIKING something, it's just acknowledging it. I happen to love Kiss, but there are plenty of bands that I really like that are influenced by bands I do not listen to and don't care for (I'm not a huge thrash fan, for example, so while DT is one of my favorite bands as well, as they progressed and incorporated more of the thrash metal influences.
I have a step daughter I've been helping raise as my own for 8 years, just to be perfectly clear. Once again, I am not stating my opinion as universal fact. The other guy above said the same thing.
I wasn't trying to dig or make it personal, but to explain myself better. I'm a massive music fan. I have a wall of CDs, I play, etc. So when my daughter started to get involved in music, I was as thrilled as anyone could be. She liked (and likes) to sing and wants to play an instrument (she's playing ukulele at school). But imagine my chagrin when she gravitated to Justin Bieber, Taylor Swift, and One Direction. And at first I tried to make sure she understood where that was coming from; when Swift played a Train song in concert then a Fleetwood Mac song, I made sure she heard the originals. Same with One D. When they did that song that sounds exactly like David Bowie's Changes, I made sure she heard that. too. But she would come home from a hard day or done with her studying, she gets the same relief and emotional lift from that music that I do from DT or Genesis or whoever. And it dawned on me, who am I to say that "sucks"? I can - and do - tell her which songs don't work for me, and why, and there are some that DO work ("Once In A Lifetime" by One D and "Wildest Dreams" are two of my favorite songs ever).
All I know, is when I hear the "In The Cage Medley" from 3SL, the hairs on my arms stand up; if that Swift song does the same thing to her, how can that "suck"? It's music, it causes the same reaction over time and space, so how does "Genesis" rule and Swift drool? It makes no logical sense. So I look at the one variable that is different, and it's ME.
This is very different than "like". I don't like those bands per se. I love the Dead (well, parts of it; the Godcheaux years, basically) and their biggest influence is probably Dylan. I still don't like Dylan, but I love how the Dead took his whatever and filtered it through their whatever and came up with something new.
Again, it's not personal, I'm not telling you you're wrong, I'm just saying I disagree strongly and giving tangible reasons why.