Setting capsule height on the Server is not replicated to the Client while the Server character is moving

Crouching on the Server is not replicated to the Client while the Server character is moving.

Reproduced in 4.7.6, 4.8.0, and Main (//depot/UE4/Promotable-CL-2591224)

1. Unzip/Open the attached project
2. PIE with 2 players
3. On the Client, press C to "crouch"
4. Move past the Server's character
5. On the Server, press C to "crouch"
6. Move past the Client's character

Result:
While moving, the Server character appears to jitter between crouching (setting a lower capsule height with a timeline/lerp) and standing on the Client. This does not occur on the Server while the Client is moving. In 4.8 and Main, there is no jitter but the character stays standing while moving, returning to a crouch when not moving.