Why is SQL Server's online indexing causing blocking?
Despite what the official documentation says, dropping a clustered index using ALTER TABLE DROP CONSTRAINT can be performed online (tested on SQL Server 2005-2014):

USE Sandpit;

ALTER DATABASE Sandpit
SET RECOVERY SIMPLE;

CREATE TABLE dbo.Test 
(
    col1 integer NOT NULL, 
    CONSTRAINT PK PRIMARY KEY CLUSTERED (col1)
);

INSERT dbo.Test 
VALUES (1);

CHECKPOINT;

BEGIN TRANSACTION;

ALTER TABLE dbo.Test 
DROP CONSTRAINT PK WITH (ONLINE = ON);

SELECT 
    [Current LSN], 
    [Operation], 
    [Transaction Name], 
    [Xact ID], 
    [Description]
FROM sys.fn_dblog(NULL,NULL) AS FD
WHERE
    FD.[Transaction Name] IS NOT NULL;

ROLLBACK TRANSACTION;

DROP TABLE Test;






Nevertheless, performing an operation online does not mean that other concurrent queries will not be impacted at all. The online operation does not take long term locks, but it may still consume considerable system resources (e.g. memory, processor, I/O). If these resources become a bottleneck, concurrent queries may experience resource-related waits.

In your specific scenario, the PAGELATCH_UP waits on PFS pages indicate latch contention on allocation resources. Any possible corrective action depends on the resource description associated with the latch waits.