It's all Star Trek to me. Star Trek is like family. I really like some of it. I can't stand some of it. But I love all of it regardless, even if it's like me telling my little sister that she needs to get her shit together. Star Trek needs to get its shit together. Whether or not it's done the way I FEEL it needs to be done, I'm not the patriarch. I will love it regardless, even if I hate it.
That being said, I think Star Trek has certain core elements that make it Star Trek and NOT BSG or Doctor Who. Does that mean it can't draw inspiration off those shows? Absolutely not. It can draw inspiration from an NFL team's history for all I care, as long as it doesn't lose the core things: character development, quality science-fiction storytelling, addressing social issues that people hesitate to talk about, and at least acknowledging where it came from if it's not going to just expand on it. That last part is tricky, because it sucks you in. DS9, VOY, and ENT (and Insurrection, Generations, and Nemesis) focused on that last part so much that it defined they dropped the first three and we, as fans, were left feeling empty. The new movies, touched on it, ST09 more than STID, but STID just barely squeaked by in acknowledgement.
So we move forward, in whatever timeline, and get back to what makes Star Trek Star Trek, and we'll be fine.