I posted this earlier in the thread, but it seems to fit here as well:
I vividly remember a TV interview Eccleston did when he took on the role (at least I think I do -- he didn't do many interviews and I've not been able to find it since, so I'm beginning to think I dreamt it) where he firmly stated that this new version of the series belonged to the children of today (i.e. 2005) just as the original had belonged to previous generations of kids. I loved that. It meant it wasn't my Doctor Who, but I had the privilege of watching it anyway. (I took that same attitude to New Dallas as well: this wasn't mine; I had no ownership of it, and somehow that made it an even more exciting experience.) I remember thinking how much kids would be loving the farting aliens, which the BBC never would have stood for when I was growing up. It wasn't until years later that I discovered how unpopular the farting aliens were with Who Fandom, who take the whole thing altogether more seriously.
It is not a matter of having to choose either the original series or the relaunched series.
That is a false choice construct. People can be fans of both.
It is true, however, that fans of the original series kept Doctor Who visible with fan sites, utub videos, fan clubs, supporting merchandising
such as DWM, novelized new adventures, DVDs, etc.
Without fans of the original series, there would have been no relaunch, or any series at all in the first place.
The new series did clearly acknowledge the classic series with Daleks, Autons, Unit, mentions of the Time Lords, reference to (unnamed) Davros
and a scene with a Cyberman helmet. The new series was successfully relaunched, because it appealed to both fans of the original series and new fans.
I disagree that fandom takes it too seriously. Most fans simply want the show to be entertaining and well produced/written.
For the most part, it was until the disastrous Chibnall/JW era, in large part because he disrespected the shows origins.
A long-running franchise, whether it is DR Who, Star Wars or Star Trek, must be grounded in a basic core story,
otherwise it is just "anything goes" which ultimately destroys the entire basis of such shows.
Now that RTD has returned and NG seems to be a charismatic actor, we will see how Doctor Who does.
Again, people can be fans of both the original series and the relaunch. It is not a one or the other choice