A quick re-write of your query to make it easier to read and interpret makes it look like this:
$qry = "SELECT p.ProjectProperty1, p.ProjectProperty2, u.UserProperty1, u.UserProperty2
FROM projects p, users u
WHERE p.ProjectProperty1 LIKE CONCAT('%', users.UserProperty1, '%') OR
p.ProjectProperty2 LIKE CONCAT('%', users.UserProperty2, '%') ,";
Where is the rest of this query? Note that I dropped your redundant 'likes' since one is as good as the other.
It does appear that you database design is flawed in that you have multiple data items of the same 'thing' stored on each record. A proper design would break those properties out to a separate table that has only one of them per record.
As for your results - without seeing the rest of the query it is hard to continue.