Couldn't replicate your results (most likely you have different individual ids on the one starting with 308....)
 
Does the result from this look correct?
Names Default To Here(1);
//https://community.jmp.com/t5/Discussions/create-new-id-to-deal-with-multiple-to-multiple-relationship/m-p/365298#M61470
/*
dt = New Table("Untitled",
	Add Rows(20),
	Compress File When Saved(1),
	New Column("Individualid",
		Numeric,
		"Continuous",
		Format("Best", 12),
		Set Values([1, 1, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 7, 8, 9])
	),
	New Column("Email_HASHED",
		Character,
		"Nominal",
		Set Values(
			{"a", "b", "a", "c", "d", "e", "f", "g", "a", "h", "i", "j", "k", "l",
			"m", "n", "o", "p", "q", "b"}
		)
	)
);
*/
dt = New Table("Untitled",
	Add Rows(19),
	Compress File When Saved(1),
	New Column("Individualid",
		Numeric,
		"Continuous",
		Format("Best", 12),
		Set Values(
			[139, 100, 229, 301, 308, 284, 682, 136, 586, 256, 122, 711, 629, 116,
			152, 443, 301, 695, 311]
		)
	),
	New Column("Email_HASHED",
		Character,
		"Nominal",
		Set Values(
			{"A648", "CAA", "E7B", "5B2", "", "237A", "", "FE0", "", "7C21", "",
			"920B", "", "D394", "", "2FE1", "", "", ""}
		)
	)
);
dt << Size Window(500,900);
dt << New Column("newid", numeric, ordinal);
//setup first values before While loop
rowList = [1];
idList = dt:Individualid[rowList,0];
emailList = dt:Email_HASHED[rowList,0];
index = 1;
//looping
While(1,
	oldRowList = rowList;
	Remove From(emailList, Contains(emailList, ""));
	rowList = dt << Get Rows Where(Contains(idList, :Individualid) | Contains(emailList, :Email_HASHED));
	//dt << Select Where(Contains(idList, :Individualid) | Contains(emailList, :Email_HASHED)); //for visualization
	//wait(1); //for visualization
	If(N Items(oldRowList) != N Items(rowList),
		idList = dt:Individualid[rowList,0];
		emailList = dt:Email_HASHED[rowList,0],
		If(All(oldRowList == rowList),
			dt:newid[rowList] = index;
			newRow = Contains(dt:newid << get as matrix, .);
			
			newRow = 0;
			For Each Row(dt,
				If(:Email_HASHED != "" & IsMissing(:newId),
					newRow = Row();
					break();
				)
			);
			
			If(newRow == 0,
				break(),
			);
			index += 1;
			rowList = Matrix(newRow);
			idList = dt:Individualid[rowList,0];
			emailList = dt:Email_HASHED[rowList,0];
		);
	);
);
//dt << Clear Select;
//handle missings
index++;
missingRows = dt << Get Rows Where(IsMissing(:newId));
dt:newId[missingRows] = index
 
					
				
			
			
				
	-Jarmo