Local sequence cannot be used in LINQ to SQL implementation of query operators except the Contains() operator

You can't use a Join between a SQL source and a local source. You'll need to bring the SQL data into memory before you can join them. In this case, you're not really doing a join since you only take the elements from the first collection, what you want is a select...where...selectid in query, which you can get using the Contains method.

 var SE = Shop.Sections.Where( s => obj.SectionObjects
                                       .Select( so => so.SectionId )
                                       .Contains( s.SectionId ))
                       .ToList();

Translates to

select * from Sections where sectionId in (...)

where the values for the in clause come from the list of ids in the collection of local objects.

You can't join local source to SQL source, but you CAN join SQL source to local, v.v.

var SE = from c1 in obj.SectionObjects
              join c in Shop.Sections on c1.SectionId equals c.SectionId
              select c;

In other words, local source must come first

This should work and be done on the database side (using IN), rather than in memory:

var SE = from c in Shop.Sections 
        where obj.SectionObjects.Select(z => z.SectionId).Contains(c.SectionId)
        select c; 

L2S Profiler is very helpful for these kinds of things - you can compare the different SQL being generated by my solution and other solutions.