Lightweight lumber or lumber alternative for building a 6'x7' portable privacy screen?
I would stick with plastic rather than wood.  It will last longer, retain its appearance, it's cleanable, it's lighter, it doesn't warp or split, and it's easy to work with.  Most of the external trim on houses is cellular PVC.  You can get thin planks or cut them from a sheet.  Companies like Azek and CertainTeed make endless varieties and are sold at building supply stores.  Chains like Home Depot and Lowes have in-house brands.

A slightly different design: use PVC slats made for "faux wood" window blinds.  The slats are very thin and light, and 2" and 2 1/2" are commonly available widths (you would just need more of them).  They are much thinner than the thinnest available trim boards and sheets, so they flex a lot more. You would probably want a solidly made frame to mount them on, with a vertical support maybe every 2' or so.

In terms of mounting the screen, wind will be a problem.  That amount of surface area will result in a lot of force when the wind blows.  It will need securing at many points, and best at the top and bottom.  I've used very heavy duty zip ties, but they deteriorate in the sun, become brittle, and break after a few years (probably sooner if under heavy stress from the wind).  You'd need to replace those each season.

Another idea: use vinyl siding for the planks.  Trim off the mounting strips so you only see the "planks".  If you are concerned about the appearance on the back side, use another set there.  Alternative: use PVC cement to glue the siding back to back to create a hollow "board".  If you don't want to see the ends, which would give away the illusion, cover the sides with a trim strip.  You can get the siding in any finish or color you want.