Indirect support
The DMG description of the Fey Crossing (page 50) says (emphasis mine)
Fey crossings are places of mystery and beauty on the Material Plane that have a near-perfect mirror in the Feywild, creating a portal where the two planes touch.
So what is a portal? Is it bidirectional, one-way only, or does it vary?
A portal is a general term for a stationary interplanar connection that links a specific location on one plane to a specific location on another (PHB301, DMG 45)
whichThe definition doesn't actually specify whether portals by their nature are uni- or bi-directional.
Of the spells in the PHB that create portals, the descriptions of Arcane Gate, Gate, and Passwall (per Prismatic Wall) are clearly bidirectional, and that of Mordenkainen's Magnificent Mansion appears to be so (presuming you can leave before the spell ends). That of Teleportation Circle appears to beis unidirectional, so perhaps a portal could be of either type.
The portal that might make a fitting "Adventure Climax" (DMG page 75) is clearly bidirectional, as is the "Dungeon: Planar Gate" (DMG page 293).
The description of the Well of Many Worlds (DMG 213) says it creates a "two-way portal" which, if not redundant, implies that one-way portals exist as well.
Given that portals conceivablyin general could be uni- or bi-directional, is there any support for Fey Crossings specifically being bi-directional?
In the lore section on redcaps in Volo's Guide to Monsters, p. 188: (emphasis mine)
In the Feywild, or where that plane touches the world at a fey crossing, if a sentient creature acts on an intense desire for bloodshed, one or more redcaps might appear where the blood of a slain person soaks the ground.
While the recapsredcaps themselves (fey creatures) are not crossing from the Feywild to the world, certainly some form of influence or essence is. That is, the act of bloodshed sends a trigger from the world into the Feywild, and the essence of the redcaps in response passes from the Feywild into the world, allowing fey creatures to grow in the soil of the connected place.
I think it is safe to conclude that at least some fey crossings would allow creatures in the Feywild to cross over to the Material, much as the essences of redcaps do. Whether or not all do would besuch crossings work like this is up to the DM Prerogative.