Why is the Brotherhood of Steel attacking me?

There's no faction impact for doing ED-E's quest line, so that's not your problem.

The problem is hard to pinpoint, since the game's scripts are very complex and there are more than a few bugs. One important note is that if you tend to wear NCR armor, don't, as the Brotherhood is hostile towards NCR.

There's a couple of reasonably surefire ways of getting into the bunker without violence, though:

• If you can, head to the 188 Trading Post and pick up Veronica who is from the bunker and can be relatively easily convinced to take you there. There's a pretty good chance that she'll be able to get you into the bunker. If you've done (or are in the process of doing) her loyalty quest, though, these paladins might be part of that. If that's the case, murder away!
• The other option is to get some faction armor for the Brotherhood. There's some at a few locations, like in the ruins outside Nellis Air Force base or REPCONN Headquarters, both of which are part of Still in the Dark

Finally, the quest here is to wipe them out, so if you're strong enough, you just might go ahead and do that. Alternatively, you can just tell Yes Man that you don't care, in which case you'll skip having to deal with them.

Around 1:30 a.m. to 3:00 a.m. around 3-6 brotherhood paladins will patrol the area, due to thier strict "isolation" policy, they will shoot you on sight. You can kill them without loss of karma or BoS reputation, Or just use a stealth boy then fast travel there or just dont fast travel there around 1:30 a.m. to 3:00 a.m. and you'll be fine, the ones in the bunker won't ever shoot you unless you give them a reason. Also I beleive if you have a positive reputation with the BoS the patrols won't shoot you on sight. Also the door to the BoS bunker's lock is very hard, so if you can't get into the bunker because your lockpick skill isn't high enough just pickpocket one key from the patrols that come out at night.