By RAW, only Medium or smaller creatures can enter
However, RAI may have been something different, as Crawford's tweet indicates. Let's look at what definitely fits and how large a Large creature is, and try to interpolate how a DM could rule.
8 Medium creatures can fit, according to the spell.
All creatures, even within the same Size category, have different sizes and weights. So to avoid comparing apples to oranges, let's look at what happens to any Medium creature affected by the Enlarge spell:
Enlarge. The target's size doubles in all dimensions, and its weight
is multiplied by eight. This growth increases its size by one
category-- from Medium to Large, for example.
Size doubling in all dimensions correlates well with the weight multiplier - doubled height, width and depth would imply a creature of eight times the volume.
So a single Large creature is as large and as heavy as 8 Medium creatures, which happen to be exactly what fits inside the space created by a Rope Trick.
So it could fit
This leaves room for DM interpretation - is the space of the proper shape to fit the creature?
- If the space is roughly spherical, there may even be some extra room under the "ceiling", previously unused by Medium creatures, leaving floor space for one or two Medium creatures.
- If the space is a tight corridor, precisely fitting Medium creatures in a row, a Large creature probably couldn't squeeze in unless very "slim" (like, say, a snake).
But can it enter?
Fitting inside is one part, the other is actually being able to enter the Rope Trick space. The spell states:
[...] [T]hose inside can see out of it as if
through a 3-foot-by-5-foot window centered on the rope.
This indicates a 3x5 foot aperture. This is explicitly a viewing window, but could reasonably to be assumed as a minimum size for the entrance, if so adjudicated by the DM.
Whatever the size of the entrance, the rules for squeezing into a smaller space\$^1\$ state:
A creature can squeeze through a space that is large enough for a
creature one size smaller than it. Thus, a Large creature can squeeze
through a passage that's only 5 feet wide. [...]
This matches up pretty well to ONE of the two dimensions of a Rope Trick opening - a Large creature could be able to squeeze through, albeit with some difficulty, if you read the "wide" as relating to "width", and not "the least of width and height".
We're getting pretty heavy into interpreting rules in a specific beneficial way, so as always, the feasibility will depend on DM ruling.
\$^1\$ Thanks to mdrichey for pointing this rule out.