Never have been able to find a final answer to this.  I'm using the Rieval hair prop but it's very difficult to use the morphs included with it because several of the layers have their normals reversed.  I have:

1:  Gone into the Advanced tab in the Materials editor.  "Normals forward" is already checked.

2.  Used the grouping tool to select all and then clicked "Reverse Normals".  That made the invisible ones visible and made the visible ones invisible.

3.  Followed Dr. Geep's advice and made a new group, added all to it, and reversed normals.  I got the same result as in number two above.

Anyone have any ideas about what to try next?

Take it into a modeler and fix the normals alignment, many modelers have an "align normals" feature that will get them all going one direction on each plane of polygons.  If you're not comfortable doing this yourself and this is a commercial item you may want to contact the vendor and ask for this, or if it's a free item you can maybe point me to it and I can probably fix it with small effort.

First, thank you very much for the advice and the offer to help!

I have Hexagon 2.  There is an option in there to "align" normals.  Would that work?  I would save the .obj with the same name, right?  Otherwise, if I save it with another name, I'll have to tweak something somewhere so it points to the new .obj, right?

Make a backup of the original OBJ, don't overwrite it without doing that first.    Otherwise yeah that should do.

Note this process of "align normals" is usually done per plane of polygons; but if you can get each plane of polys aligned, then it shouldn't be a big deal to manually select each plane's polygons and then reverse their normals in Hexagon.

Didn't work.
I brought the geometry into Hexagon and selected "select all".  Then I went to tools and utilities and clicked "orient normals".  In the properties pane I clicked "unify normals" and saved it under it's original name (I made a backup).  But when I load it in Poser, there is no change.

There are three layers in the Rievel hair: scalp, hair1 and hair2.  Is there any way of selecting the layers individually?  Anything else I can try?

Poser has the make normals consistent feature, when you import a prop.
Not sure how the prop's textures would survive.

The textures are fine.  That's never been a problem.  There's just no change to the reversed normals when I load the prop.  Even when I import the .obj as a static, morphless prop (with normals consistent), half the normals are reversed.  In every instance, "normals forward" is checked in the advanced tab of the material room.

Is this a commercial item or free?

It's a commercial item.  Are you going to suggest contacting the vendor?

Try using one of the other preview display modes for the hair prop/figure, e.g. cartoon/cartoon with lines or hidden surface.

Quote - Try using one of the other preview display modes for the hair prop/figure, e.g. cartoon/cartoon with lines or hidden surface.

Well, if it's hidden, I can't see it to morph it.  In some modes it's totally transparent.  In most modes, only some of it shows, which is the problem in the fully textured mode.  The one  mode where all normals seem to show is the cartoon w/lines mode, but that's a mess to see and use.

Quote - It's a commercial item.  Are you going to suggest contacting the vendor?

Yes, they really should fix something like this.

I just sent a private message to the vendor.  Of course, I only wanted to do that as a last resort, not because I'm afraid to, but because by asking here and elsewhere, I might get to learn something in the process.  I feel pretty comfortable now that I've exhausted that avenue, so thank you to all of you who responded.  I really appreciate the time you took.

Why would you be afraid to ask for this?  You paid money for it, and it's a very reasonable thing to ask for.  Although it will help you in the long run to figure out how to do this, it will probably be easier to learn it on a less complex model (and one you didn't pay money for).

Oh I'm not afraid to ask.  I just did!  What I meant was that I would be hesitant to ask the vendor without first trying to find out myself.  Now I can say I did try first.