A boggle uses its dimensional rift capability to partially appear next to a PC and attack it. When the boggle retracts his arm and upper body back through the rift, would it allow an opportunity attack?
I found one single web page stating that it wouldn't but it doesn't give any rules reference or explanation as to why it wouldn't do so.
I agree with the rules interpretation of this answer. An opportunity attack occurs "…when a hostile creature that you can see moves out of your reach." The Boggle's withdrawal after an attack does not involve moving out of the target's reach, so no opportunity attack is made on that basis.
I disagree with the other answer that this is merely a technicality and that opportunity attacks could be allowed for this use of dimensional rift.
First, I observe that an opportunity attack is not just about moving out of reach. That is a necessary but not sufficient condition. The creature moving also must do so without taking the Disengage action, and without having any other feature that would limit or eliminate opportunity attacks against them (e.g. Barbarian's third-level Eagle Spirit totem, which imposes disadvantage to opportunity attacks against the Barbarian).
There are clearly a number of specifics in the rules that offset the "moving out of reach" aspect that would normally allow an opportunity attack.
Second, it is not a logical inconsistency that an opportunity attack depends on moving out of reach but must take place before the creature is actually out of reach.
Indeed, the presence of the Disengage action makes more clear why an opportunity attack happens. It is not the movement itself, but the nature of the movement. I.e. to move away from a hostile creature in an unguarded way. The entire movement is done in an unguarded way and thus invites the opportunity attack.
The risk to the moving creature is present as soon as they try to move, thus the attack can occur before they actually move away.
The action economy is used to balance this risk, by allowing a creature to spend an action to eliminate it. Narratively, this movement is done more carefully, in a way that prevents the opportunity attack. It doesn't mean there's an inconsistency between the rules and the narrative movement.
Likewise, it's easy to see that the Boggle is not really moving away per se, and does not have the unguarded aspect of their movement. They are no more moving away than a fighter is moving away after they attack with a sword when they bring their sword back close to their body. Even taking into account that the Boggle ultimately winds up inaccessible by the target of their attack, there's no inconsistency in disallowing an opportunity attack on the Boggle as they finish their attack and move back to the other side of the rift.
See also e.g. Boggle Tactics for another unofficial interpretation along these lines:
A boggle may open a Dimensional Rift (bonus action) that allows it to reach a victim and pummel him or her through the rift (Attack action), then run away (movement). It can do so without incurring an opportunity attack, because the target can’t attack back through the rift!
Note that opportunity attacks are provoked when you leave a creature's reach:
You can make an opportunity attack when a hostile creature that you can see moves out of your reach.
Meanwhile, the Boggle's Dimensional Rift feature states:
[...] While next to the rift, the boggle can see through it and is considered to be next to the destination as well [...]
Thus, the Boggle is considered to be in two places at once and because of this, when it goes through the Rift and later goes back through it the other way, nothing actually changes. The Boggle has not moved and the locations it is considered to be in have not changed.
Technically, thus means an opportunity attack is provoked when the Boggle moves from the other side of the Rift to a new location (assuming the creature on the other side can see the Boggle), but this usually won't do anything since only the Boggle can use the Rift (I say "usually" because things like War Caster exist).
While the above interpretation is, to me, compliant with the actual rules, it doesn't make a ton of sense. If you can attack somebody who walks away from you before they actually leave your reach, you should similarly be able to attack a creature who Dimensionally Rifts away from you before they use the Rift (note, the Rift does not use movement in the game-sense of the word but it does involve moving in the English sense of the word and these can be contrasted with teleporting, which is instantaneous). At my own tables, I have not used a Boggle, but I would allow for opportunity attacks to be made against them. (I would also likely rule that the first time the Rift is used, it is such an unexpected attack that the character being attacked could not attack back).
