Leomund's Tiny Hut does not block planar travel or teleportation
Teleportation and planar travel are effects that are specifically blocked by higher-level spells such as Mordenkainen’s Private Sanctum, which can create these effects (among others) within its area:
- Nothing can teleport into or out of the warded area.
- Planar travel is blocked within the warded area.
Several other higher-level spells can create similar effects, but the text of Leomund's Tiny Hut doesn't contain anything like this. Private Sanctum, at 4th level, is the lowest-level spell I can think of that can block planar travel.
So, to the extent that conjuration involves summoning something from another plane, such an effect would not be blocked by the hut, with one important exception:
Leomund's Tiny Hut prevents entry via the Ethereal Plane
Leomund's Tiny Hut creates a dome of magical force, and according to the DMG, all creations of magical force extend into the Border Ethereal:
Normally, creatures in the Border Ethereal can’t attack creatures on the overlapped plane, and vice versa. A traveler on the Ethereal Plane is invisible and utterly silent to someone on the overlapped plane, and solid objects on the overlapped plane don’t hamper the movement of a creature in the Border Ethereal. The exceptions are certain magical effects (including anything made of magical force) and living beings.
So if a spell were to attempt to summon a creature from the Ethereal Plane, the spell would be unable to do so unless the creature to be summoned was already inside the dome at the time Leomund's Tiny Hut was cast.
However, all of the above may be irrelevant, because:
Conjuration spells do not necessarily involve planar travel
Many conjuration spells that summon creatures don't specify a mechanism by which those creatures are summoned. For example, the relevant part of Conjure Animals reads:
You summon fey spirits that take the form of beasts and appear in unoccupied spaces that you can see within range.
How do the creatures get there? "You summon" them. That's all it says. Given that no mechanism is specified, the manner by which creatures are summoned by conjuration spells is left entirely up to the DM. Of course, given that the creatures summoned are "fey spirits", it would be perfectly reasonable to the DM to rule that the spirits are summoned from the Feywild and must therefore be summoned from one plane to another. So you should check with your DM about how they plan to handle this. (Worth noting: supposedly these kinds of spells tend to cause DMs a lot of headaches, to make sure to ask nicely.)
In any case, if your DM rules that summoning involves planar travel, then the above 2 sections should have you covered. (Likewise, the above sections apply to any conjuration spell that does explicitly call a creature from another plane, of which there are a few.) And if your DM rules that summoning doesn't involve planar travel, then you've got nothing to worry about. In fact, you don't even have to worry about the 9-creature "occupancy limit" of Tiny Hut, since that only applies at the time of casting. (Any creatures summoned into the hut would, however, be trapped inside until the spell ends.)