The rubble is there to prevent the jagged crown quest from becoming glitched if you visit it beforehand, Once the mission for the jagged crown is initiated by meeting the other guards outside, and listening through the conversation, the rubble vanishes, and you can continue ahead of the soldiers if you wish to. There isn't any other way in or out that i've found inside there, and believe me I've tried, I love the crown its awesome looking.

If the game glitches, attempt to talk to the Officer who is leading the group (storm cloak / imperials), if he isn't around head back to where you are to meet up with them outside, a oddity can happen where none of them are there, but the voice dialog will still play through. Also its a good idea not to go inside till after the leader makes his little speech outside the door, jumping the gun here can also lead to a glitch.

Killing off all the bandits prior to entering the crypt, even killing off all the storm cloaks / imperials standing outside of the crypt before meeting up with the group, doesn't seem to glitch the game, but advancing inside during the mission prior to meeting up with them seems to have a 50/50 chance of glitching it. If the rubble doesn't get removed there isn't any way to continue it unless you can glitch yourself through the rubble, but then, you can end up with the same problem leaving as well, as the entrance may end up still being blocked with rubble.

Try to get yourself the "Clarvoyance" spell ability which allows you to cast a spell that shows you the path you need to follow through any dungeon or quest. It has been indispensable for me in finding the way through many of the more ticky dungeons. I don't use it all the time, only when I get stuck and can't figure out where I am supposed to go next.

Clairvoyance just leads me straight into the impenetrable wall. I've gone back and and forth outside the entrance looking for another way in- no dice. this is a pretty big glitch, the civil war quest line cannot proceed any further. I'm level 56 and kind of don't want to try an earlier save! CR4P!

i left Skyrim alone for a few months hoping that a lot of the quest breaking issues I have would be fixed with a few patches.
It's now mid-April and this significant bug is still not fixed.
I'm pretty disappointed.

Because I'm now an empire-loving Altmer. My first character was a Nord, and of course I sided with Ulfric.

I went to Korvanjund early with my Nord, and found the rubble blocking the way, just as you did. I figured there must be another entrance into this dungeon, so I went back outside and hunted all over for it. No luck, of course. So I left and forgot about the place. Much later, I came back to it as part of the main quest line, and the rubble was magically gone. I was able to proceed normally. This was all under Version 1.4. We'll see what happens with 1.5, my new character and empire allies rather than stormcloack.

I'm sorry you ran into this showstopper. It brings back memories of having to start a whole new game in Oblivion to be able to play the Shivering Isles expansion. I ran into the felldew bug, and didn't realize it until much, much later.