Try this instead, see if it's any faster:

SET NOCOUNT ON;

IF OBJECT_ID(N'tempdb..#output') IS NOT NULL

DROP TABLE #output;

CREATE TABLE #output (line VARCHAR(255))

INSERT INTO #Output

VALUES ('<?xml version="1.0"?>'),

('<Objects>'),

(' <Object>'),

(' <Property Name="Folder">\\SERVER1\Clients\APHE\Accounts</Pr'),

('operty>'),

(' <Property Name="Access">Modify, Synchronize</Property>'),

(' <Property Name="User">Domain1\User3</Property>'),

(' </Object>'),

(' <Object>'),

(' <Property Name="Folder">\\SERVER1\Clients\APHE\Location</Property>'),

(' <Property Name="Access">Modify, Synchronize</Property>'),

(' <Property Name="User">Domain1\User3</Property>'),

(' </Object>'),

(' <Object>'),

(' <Property Name="Folder">\\SERVER1\Clients\BPE\Accounts</Pr'),

('operty>'),

(' <Property Name="Access">ReadAndExecute, Synchronize</Property>'),

(' <Property Name="User">Domain1\User2</Property>'),

(' </Object>'),

(' <Object>'),

(' <Property Name="Folder">\\SERVER1\Clients\BPE\Location</Pr'),

('operty>'),

(' <Property Name="Access">Modify, Synchronize</Property>'),

(' <Property Name="User">Domain1\User1</Property>'),

(' </Object>'),

(' <Object>'),

(' <Property Name="Folder">\\SERVER1\Clients\BPE\Comments</Pr'),

('operty>'),

(' <Property Name="Access">ReadAndExecute, Synchronize</Property>'),

(' <Property Name="User">Domain1\User2</Propert'),

('y>'),

(' </Object>'),

(' <Object>'),

(' <Property Name="Folder">\\SERVER1\Clients\PRD\Accounts</Pr'),

('operty>'),

(' <Property Name="Access">ReadAndExecute, Synchronize</Property>'),

(' <Property Name="User">Domain1\User3</Propert'),

('y>'),

(' </Object>'),

('</Objects>');

SELECT item.ref.value('(Property/text())[1]', 'nvarchar(200)') AS Folder,

item.ref.value('(Property/text())[2]', 'nvarchar(500)') AS Access,

item.ref.value('(Property/text())[3]', 'nvarchar(200)') AS UserGroup

FROM (SELECT CAST((SELECT '' + line

FROM #output

FOR XML PATH(''),

TYPE).value('.[1]', 'varchar(max)') AS XML) AS FormattedXML)

AS Sub

CROSS APPLY FormattedXML.nodes('/Objects/Object') AS item (ref);

Ignore the part that constructs the test data, of course. It's just the final query that matters.

It uses a For XML Path trick that concatenates strings together. It's documented behavior, and nicely replaces the cursor.