Disclaimer: This is my first bug report.

You cannot sit or stand invulnerable wolves.

How to Recreate Glitch #1:

1. /summon minecraft:wolf ~ ~ ~ {Invulnerable:1}
2. Tame it or add Owner tag to summon command
3. Try to sit it

How to Recreate Glitch #2:

1. Spawn a wolf and tame it then go near it and run this command
2. /data merge @e[type=wolf,sort=nearest,limit=1] {Invulnerable:1}
3. Try to sit it