E T   Mahogany for the stiles and rails would work fine, for the flat panel maybe a glue up of the same material would work.
My concern would be the paint adhering to the mahogany because of the oils in the wood.

Thanks for the input.

I could be wrong but I think south American mahogany paints well.  Feel free to correct me on that.

Anyone want to weigh on gluing up the flat panels.  That was my first thought but I wonder how well they'd hold up being that large. (warp, cup, split?)

I prefer real wood every chance we get but...

Is MDO plywood a bad idea for the panels?

I have. Any wood that is going to be outside will need some maintaining every year. It you are going to use paint, I can see no reason to use more expensive wood, because the paint is going to cover it, unless you have a bunch of that wood laying around. Assuming it is going to be painted, I would use plywood or MDO, but the ply would be cheaper.

If it is not going to be painted, I would us Ipe or Sapele. Both stand up to the weather really well. You will run into problems with thin panels from solid wood in a outdoors environment and having to repairs in a year or less.

i would use marine ply for the panels and plant on ipe or teek etc.

another option would be some of that plastic or cement board fasia board stuff and domino it together

I say forget the mahogany, there are less expensive alternatives that will work just as well (or better).  Cypress if you can find it in your area is a very good choice.  Other woods that will work well, spanish ceder and white oak.  White oak is least expensive but it's also heavy (that's not necessarily a bad thing).  I'd stay away from poplar, there's no reason to tempt fate when the client has the budget for better material.  

Brice,

If he's matching the color to what's in the picture, it's too dark for Azek or other PVC brands.  The heat from the sun will do all sorts of funky things with the PVC when painted too dark.  That's why on the tech instructions for the manufacturer's website, they usually state a light reflective value range.  I was recently told by one manufacturer, the color you choose (too dark) could void the manufacturer's responsibility after install.

Timberlane has a line of shutters that they do this with.  After examining how they did it I found that they put some aluminum channel laminated between 2 pieces of azek for the rails and stiles.  We hung some black shutters for a customer about 4 years ago and they still look as good as the day we hung them.  I have never had a problem painting Azek some very dark colors so long as you do the proper prep and use the right paint.  We are actually in the process of designing a large pergola all of PVC and will be laminating site made plywood beams into 2 layers of 5/4 PVC for the rafters.  Ill make sure to post pics when we get started should be a fun one.

Fully realize the manufacturers don't like dark colors, but if a VERY reputable company like Timberlane can make a shutter out of Azek, (I know this because was i was at the factory), and offer a lifetime warranty with it even when painted black I would tend to think it can be done.  I just trimmed, last year, the entire exterior of a house, all beaded and jack mitered with a plank molding and they painted it a dark green.  Glued and pocket screwed all joints and it still looks like new.  Sherwin Williams Duration paint has ALOT of stretch to it.  I tend to think that no matter the color if its plastic and its in the sun it is going to get hot, you just have to allow for it to move (Lots and lots)  and you will be ok.  Don't get me wrong I would much rather work in wood, but sometimes it just makes sense.

Sorry, my Azek suggestion has gotten this thread a little off course...

Brice,

I don't think that your suggestion has gotten this off course at all.  Material choices are what were asked for, and you supplied a very viable material.  Color choices and products and warranties are all part of the equation.

Peter

Definitely agree Brice.  I'm not really ruling anything out.  Thanks for the input.

My first thought for heavily exposed areas is always cedar. Western red cedar seems to be the preference in the US. It holds paint well (if the moisture level is correct)  and it a joy to mill. It's a little soft for heavily trafficked fixtures like gates etc. but I still like it.
Folks here (North East) use MDO for exterior, but the construction is not true rail and stile but an applied rail and stile design where the rails and styles are over laid, glued and pinned to a large panel creating a rail and panel look. The edges are usually covered with a poplar molding and then primed.
Pine (ponderosa)  is also used in exterior applications here, I am not a big fan of it but some of the window makers use it.
Heart pine (reclaimed) maybe another alternative. It is almost as  hard as Red oak.



I think mahogany is a bit of overkill but I can see why you would use it. Unless this is going to be a clear finish and you can see the wood it just seems unnecessary though. There was a good discussion about choice of wood, construction techniques etc. for an  Arched Gate on Wood web.



Money is always an issue 
I think the paint (color and adhesion) because of UV will be the number one issue here particularly on a south facing (in direct sunlight) wall.
Folks recommend Sikkens Cetol system for this situation although I have never used it so I can't recommend it. It looks like this shutter is failing due more to lack of maintenance than any thing else, so you may want to include a maintenance schedule (option) in your pricing.



Depending on what material you use I (mdo, PVC solid wood) I would favor mortise and tenon of which you have had plenty of great advice already. I think you do need to think about the drainage on the bottom rails if your profile is at right angles to the face.

Tim