How to make your player invincible / undetectable by zombies?

Create a team:

1.13+: /team add friendly
1.12-: /scoreboard teams add friendly

Join the team:

1.13+: /team join friendly
1.12-: /scoreboard teams join friendly

On a clock, make all zombies join the team:

1.13+: /team join friendly @e[type=zombie]
1.10-: /scoreboard teams join friendly @e[type=Zombie]

Mobs in the same team as you will not attack you.