What I expected to happen was...:
In 1.13 riding a boat into a end gateway block with a command specified teleport target would teleport the boat and player to the target coordinates.
What actually happened was...:
The end gateway block registers that an entity enters it but does not teleport the boat until the player dismounts it.
Steps to Reproduce:
1. Create an end gateway in a flat-world with the command: "/setblock 0 10 0 minecraft:end_gateway{ExactTeleport:1b, ExitPortal:{X:0, Y:10, Z:10}} destroy".
2. summon a boat with command: "/summon minecraft:boat ~ 10 ~ {NoGravity:1}".
3. Right click boat to ride it, and drive it into the end gateway collision box.
Related issues
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Comments

@unknown, this ticket is about players not being able to enter end gateways in a boat, not entities.
Cannot reproduce in 20w14a.

I can confirm for 1.16.3 but results are pretty inconsistent. Sometimes you would teleport but still stay in the same place, sometimes it just doesn't work and sometimes it works.
Can confirm in 20w51a.

Can confirm in 1.17.1. Sometimes this causes a desync and the player visually falls into the void and gets softlocked (MC-193114). In some cases it does work though.

This seems to have been fixed between 21w37a and 21w41a.

Still cannot reproduce in 1.19.2. Can anyone still reproduce this issue in 1.19.2?
Can confirm. I cannot transport a shulker in a boat through an end gateway portal. The shulker disappears, only the boat travels through the portal.