I spoke with Serana at the Dawnguard tower and she told me to leave Lydia behind and meet her at the docks by castle Volkihar. After that, I took Lydia to find the Dragon Elder Scroll and then accidentally brought her to the dock with me. Serana gave me the same speech about having to leave the 'interloper' behind, so I went back, dropped Lydia off at Icewatter Jetty and returned. I went back to Serana but she said the same thing. So I backed up a a few saves so that Lydia never came to the dock with me, but Serana still will not let me proceed.

Any ideas / help?

Got the exact same problem and can` find solution anywhere. Wonder if they will bring out a patch?

You have dismissed your follower so she goes home?

Otherwise you could try restarting the console and loading an earlier save before Serana mentioned anything about your follower, and make sure you dismiss your follower before speaking with Serana.

I have the problem as well. I made all my followers refollow me and then sent them home. But every time I talk to serana in fort dawnguard she tells me to get rid of the interloper. I already looked at the docks that shes supposed to take me to but nothing happens since shes not there.

i got the same problem on PC. solved in the following way (you must have "talk to serana" as quest object):
- went to breezehome and left my followers waiting there
- travelled to Volkihar doks
- opened console an wrote "setstage dlc1vq04 20" (without quotes)
- close console and wait few second

From my understanding the OP seems to be telling Lydia to "wait". At that point you still have Lydia as a follower, she's just waiting for you. You have to actually dismiss her, tell her it's time for us to part ways. Now if you've done that and Serana still isn't happy.. I'm not sure.