D&D 5e's Player's Handbook says that a natural 20 when rolling an attack automatically hits (page 194). In the following section about attacks, the book describes both the grapple and shove as "a special melee attack" (page 195).
I'm aware that attacks are the only types of rolls in 5e that automatically succeed or fail on a natural 20 or 1 (death saves seem to be the only other roll with special rules for natural 20s or 1s). The core question is whether grapple and shove count as attacks for purposes of these rules.
Best Answer
No, they don't auto-succeed
Crit successes and failures only apply to attack rolls (PHB p. 194, Attack Rolls subsection).
Even though grapples and shoves are a "special melee attack" (PHB p. 195), they are not resolved by making attack rolls. Therefore, the specific rule regarding crits does not apply to them.