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Assume the party has cast Rope Trick, entered the extradimensional space and a party member is trying to block the entrance. Can a creature from outside force its way in somehow?
Does the answer differ if you consider the opening is horizontal or vertical? Does it differ if the intruder is Large, not Medium or Small?
Enemies can climb up and enter by RAW. You can't attack out of the space to do an attack of opportunity or grapple on anyone trying to enter, so they can freely enter even if you try to stop them unless you have 8 medium creatures inside. As your source notes
The extradimensional space can be reached by climbing to the top of the rope. The space can hold as many as eight Medium or smaller creatures. The rope can be pulled into the space, making the rope disappear from view outside the space.
Attacks and spells can't cross through the entrance into or out of the extradimensional space, but those inside can see out of it as if through a 3-foot-by-5- foot window centered on the rope.
Grapples and attacks of opportunity use the attack action, so you can't use them to block enemies from entering a rope trick.
When you want to grab a creature or wrestle with it, you can use the Attack action to make a special melee attack, a grapple. If you're able to make multiple attacks with the Attack action, this attack replaces one of them.
Large creatures can't enter, but they could theoretically stick a hand inside and then use an attack once inside, but that would depend on DM discretion as to what counted as inside or out. You could also let the player be half inside and out and so grapple people to prevent them from entering, but this would again be up to DM discretion on what happened.
As noted in other answers, it's not possible to launch attacks through the portal created by the Rope Trick spell. It is, however, possible to attack creatures on the same side of the portal.
So, you can simply stand by the entrance and Ready a Shove action to Shove a creature that has entered the space back through the portal.
Before we dive in, can a creature from the inside even try to block the entrance?
The the entrance size is not explicitly defined, but as you can look out through it as if through a 3-foot-by-5-foot window, I think it is save to assume that it is 3x5 feet large.
A medium or small creature can position themselves on the space on inside of the entrance. It does not matter if the entrance is oriented towards the bottom, or sideways, as creatures control a 5x5 foot space they occupy, and there would at least be 2 feet of ledge to stand on in that space if the entrance is only 3 feet wide. A creatur controls the space it is occupying. So yes, they can block the entrance by controllng the space on the inside.
Rope Trick states:
The space can hold as many as eight Medium or smaller creatures.
If the Rope trick is already filled to the brim with creatures, that is, all the space is taken up, there is no unoccupied space, and since the rules (p. 191 PHB) state that "Whether a creature is a friend or an enemy, you can’t willingly end your move in its space.", you cannot move in, as you would need to end your move on another creature's space.
Some people also interpret this sentence from Rope Trick to mean that only Medium or Small creatures can even enter the space. That is clearly not the designer's intention, so I will also consider how it works for Tiny or Large creatures, and you can ignore those sections if you feel that they cannot, but I want to provide a complete answer also for those that allow other sizes of creatures to enter.
The key sentence is this one:
Attacks and spells can't cross through the entrance into or out of the extradimensional space, but those inside can see out of it as if through a 3-foot-by-5-foot window centered on the rope.
First, you cannot shove the blocker out of the way. Shoving a Creature states (p. 195 PHB):
Using the Attack action, you can make a special melee attack to shove a creature, either to knock it prone or push it away from you.
Attacks cannot cross the entrance, and since shoving is an attack, so you cannot shove through the entrance.
Second, you cannot move through the blocker's space. Moving Around Other Creatures rules (p. 191 PHB) state:
you can move through a hostile creature's space only if the creature is at least two sizes larger or smaller than you.
So if the space is occupied by a medium or small creature, another medium or small creature cannot move through their space, as they are not two size categories larger or smaller than the creature blocking the entrance. By standard rules this means such creatures cannot force their way in.
If you allow other sizes to enter: A Tiny creature could move in, if the entry was blocked by Medium or larger creature. A Large creature could move in, if the entry was blocked by a Small or Tiny creature.
I'll consider "forcing" your way in as any means to enter the space against the will of the creature blocking the entrance. The DMG has these action options on page 272:
Overrun When a creature tries to move through a hostile creature's space, the mover can try to force its way through by overrunning the hostile creature. As an action or a bonus action, the mover makes a Strength (Athletics) check contested by the hostile creature's Strength (Athletics) check. (...) If the mover wins the contest, it can move through the hostile creature's space once this turn.
Tumble A creature can try to tumble through a hostile creature's space, ducking and weaving past the opponent. As an action or a bonus action, the tumbler makes a Dexterity (Acrobatics) check contested by the hostile creature's Dexterity (Acrobatics) check. If the tumbler wins the contest, it can move through the hostile creature's space once this turn.
These are not attacks, they are contested skill checks. Because they are neither attacks nor spells, they work across the entrance. Either one would allow you to move through the blocking creature's space and enter the Rope Trick, if you win the contest (and there is space left to move into).
Rope trick explicitly describes its method of entry:
The extradimensional space can be reached by climbing to the top of the rope.
You can’t just walk to extradimensional spaces. Game features creating extradimensional spaces that connect to your current plane always tell you how they are connected and how they are accessed. Consider the portable hole:
You can use an action to unfold a portable hole and place it on or against a solid surface, whereupon the portable hole creates an extradimensional hole 10 feet deep. The cylindrical space within the hole exists on a different plane, so it can’t be used to create open passages. Any creature inside an open portable hole can exit the hole by climbing out of it.
Can you force your way into a portable hole without unfolding it and putting it on the ground? Of course not. The extra dimensional space created by rope trick “can be reached by climbing to the top of the rope”. Just as you cannot enter a portable without entering in the way its description says you can, you can only enter the space created by rope trick except by doing so the way its description says you can. If the rope is successfully pulled into the space, it cannot be accessed from the outside, except by other means that explicitly allow interdimensional travel.
