By RAW, 60'

I'm assuming this would work via the fact that the Grappler feat doesn't slow your movement, characters can willingly fail saves, and that a character can release a grappled target whenever they want.

Yes, this works from a RAW perspective.

• Turn 1: Bob using his Action grapples Alice; Alice willingly fails her save and becomes grappled; Bob moves himself and Alice 30'; Bob releases the grapple.
• Turn 2: Alice uses her Action to grapple Bob; Bob willingly fails his save and becomes grappled; Alice moves herself and Bob 30'; Alice releases the grapple.

In total, they moved 60' (both had to use their Action to initiate the grapple, so it was unavailable to Dash).

But remember that the DMG explicitly says you shouldn't allow peasant railguns

While this kind of exploit doesn't meet the cheese threshold of the peasant railgun, you should be aware that the DMG does specifically advise against allowing this kind of loophole:

Rules Aren’t Physics. The rules of the game are meant to provide a fun game experience, not to describe the laws of physics in the worlds of D&D, let alone the real world. Don’t let players argue that a bucket brigade of ordinary people can accelerate a spear to light speed by all using the Ready action to pass the spear to the next person in line. The Ready action facilitates heroic action; it doesn’t define the physical limitations of what can happen in a 6-second combat round.

So your DM would be on firm ground to disallow this kind of exploit.

By RAW, 60'

I'm assuming this would work via the fact that the Grappler feat doesn't slow your movement, characters can willingly fail saves, and that a character can release a grappled target whenever they want.

Yes, this works from a RAW perspective.

• Turn 1: Bob using his Action grapples Alice; Alice willingly fails her save and becomes grappled; Bob moves himself and Alice 30'; Bob releases the grapple.
• Turn 2: Alice uses her Action to grapple Bob; Bob willingly fails his save and becomes grappled; Alice moves herself and Bob 30'; Alice releases the grapple.

In total, they moved 60' (both had to use their Action to initiate the grapple, so it was unavailable to Dash).

But remember that the DMG explicitly says you shouldn't allow peasant railguns

While this kind of exploit doesn't meet the cheese threshold of the peasant railgun, you should be aware that the DMG does specifically advise against allowing this kind of loophole:

Rules Aren’t Physics. The rules of the game are meant to provide a fun game experience, not to describe the laws of physics in the worlds of D&D, let alone the real world. Don’t let players argue that a bucket brigade of ordinary people can accelerate a spear to light speed by all using the Ready action to pass the spear to the next person in line. The Ready action facilitates heroic action; it doesn’t define the physical limitations of what can happen in a 6-second combat round.

So unusual acceleration due to quirks in the rules should generally be disallowed.

and also:

Combat Is for Enemies. Some rules apply only during combat or while a character is acting in Initiative order. Don’t let players attack each other or helpless creatures to activate those rules.

In general, you shouldn't be using combat rules to engage in exploits with members of your party.

Rules Rely on Good-Faith Interpretation. The rules assume that everyone reading and interpreting the rules has the interests of the group’s fun at heart and is reading the rules in that light.

If it doesn't make logical sense logically, it's probably not the intent of the rules.

So your DM would be on firm ground to disallow this kind of exploit.

By RAW, 60'

I'm assuming this would work via the fact that the Grappler feat doesn't slow your movement and characters can willingly fail saves as well as release a grappled target whenever you want.

Yes, this works from a RAW perspective.

• Turn 1: Bob using his Action grapples Alice; Alice willingly fails her save and becomes grappled; Bob moves himself and Alice 30'; Bob releases the grapple.
• Turn 2: Alice uses her Action to grapple Bob; Bob willingly fails his save and becomes grappled; Alice moves herself and Bob 30'; Alice releases the grapple.

In total, they moved 60' (both had to use their Action to initiate the grapple, so it was unavailable to Dash).

But remember that the DMG explicitly says you shouldn't allow peasant railguns

While this kind of exploit doesn't meet the cheese threshold of the peasant railgun, you should be aware that the DMG does specifically advise against allowing this kind of loophole:

Rules Aren’t Physics. The rules of the game are meant to provide a fun game experience, not to describe the laws of physics in the worlds of D&D, let alone the real world. Don’t let players argue that a bucket brigade of ordinary people can accelerate a spear to light speed by all using the Ready action to pass the spear to the next person in line. The Ready action facilitates heroic action; it doesn’t define the physical limitations of what can happen in a 6-second combat round.

So your DM would be on firm ground to disallow this kind of exploit.

By RAW, 60'

I'm assuming this would work via the fact that the Grappler feat doesn't slow your movement, characters can willingly fail saves, and that a character can release a grappled target whenever they want.

Yes, this works from a RAW perspective.

• Turn 1: Bob using his Action grapples Alice; Alice willingly fails her save and becomes grappled; Bob moves himself and Alice 30'; Bob releases the grapple.
• Turn 2: Alice uses her Action to grapple Bob; Bob willingly fails his save and becomes grappled; Alice moves herself and Bob 30'; Alice releases the grapple.

In total, they moved 60' (both had to use their Action to initiate the grapple, so it was unavailable to Dash).

But remember that the DMG explicitly says you shouldn't allow peasant railguns

While this kind of exploit doesn't meet the cheese threshold of the peasant railgun, you should be aware that the DMG does specifically advise against allowing this kind of loophole:

Rules Aren’t Physics. The rules of the game are meant to provide a fun game experience, not to describe the laws of physics in the worlds of D&D, let alone the real world. Don’t let players argue that a bucket brigade of ordinary people can accelerate a spear to light speed by all using the Ready action to pass the spear to the next person in line. The Ready action facilitates heroic action; it doesn’t define the physical limitations of what can happen in a 6-second combat round.

So your DM would be on firm ground to disallow this kind of exploit.