When an avatar uses cloth component at it's spawn - like cloth being loaded as soon as avatar loads - it causes nametag and chat bubble to appear at a higher position.
I managed to find a workaround by adding a delay to outfit's activation so it wont load with my avatar at the same time. The cloth component is always on, but outfit gameobject itself is enabled after 0.2 seconds.
I hope VRChat team can track this down.
Thanks!