Alternatives to "OR" in where clause
I think that you can rewrite that query to use a FULL OUTER JOIN:

SELECT  ordIdent.Identifier, ord.OrderId
FROM    OrderIdentifier ordIdent
        FULL OUTER JOIN [order] ord
            ON ordIdent.OrderId = ord.OrderId
            AND ( ordIdent.Identifier = '29584'
                    OR ord.ClientOrderId = '29584')
WHERE ordIdent.Identifier IS NOT NULL AND ord.OrderId IS NOT NULL;


But why would you want to? You'll end up reading all rows from both tables with that syntax which causes the performance problem that you're trying to avoid. UNION or UNION ALL is the right way to go here. For filters like you have you can still use UNION ALL like so:

SELECT  ordIdent.Identifier, ord.OrderId
FROM    OrderIdentifier ordIdent
        JOIN [order] ord
            ON ordIdent.OrderId = ord.OrderId
WHERE   ord.ClientOrderId = '01193504' 

UNION

SELECT  ordIdent.Identifier, ord.OrderId
FROM    OrderIdentifier ordIdent
        JOIN [order] ord
            ON ordIdent.OrderId = ord.OrderId
WHERE   ordIdent.Identifier = '01193504' AND (ord.ClientOrderId 
 IS NULL OR ord.ClientOrderId &lt;&gt; '01193504')


Sometimes there's a slight performance benefit in doing so. It depends on your data.