Poplar grain showing through paint

Poplar is a relatively soft wood.  Since you're finishing with a waterborne finish (Target), you should seal the wood first to prevent the water from swelling the softer summer grain.  Since your photo  shows the rails and styles, I suggest you sand them back with 320, then use a solvent sanding sealer like dewaxed shellac or rattle-can lacquer, let them dry for a full day, then lightly resand with 400 paper and try your top coat again.  Can't help with ridges in the door panels, except to sand flat and retry.

I've done a number of cabinets with General's pigmented gloss Enduro poly, but I was working with maple rather than poplar.

@Mark Mandell

Thanks.  
  I am practicing on this set, and it will end up in the shop.  The center panel is a piece of plywood, and I knew it would look different.  The rails and styles is what caught me off guard.  I have some shellac I can use to seal it.  Then repaint.

Thanks Again.

Remember to re-sand.  Consider a sanding block rather than a power sander.  A block's hard surface will make it easier not to sand dips into the summer grain.

Poplar's softness can make it harder to get a smooth surface

Not at the same level of craftsmanship you are showing, but many years ago as a home builder I finished closet knotty pine shelving boards by smearing the entire surface with drywall compound, letting it dry, sanding, and coating with Kilz original primer, not the water based stuff. Then sanding the Kilz lightly with 320 sand paper and painting.  Did a remarkable job or filling the defects and hiding the knots and grain.

You probably don't have knots to deal with or the extractive bleeding but the heavy bodied Kilz did a good job of obscuring the grain.  Since your cabinets with be subject to more wear than shelves you might want to find a tougher filler than drywall compound, Maybe Famowood or even Bondo.

Rather that trying to completely obscure the join between the rail and style you might try putting a tiny Vee groove and celebrating it.  Many commercial cabinets are done that way.

Something to play with.

@Barry Irby

I like this idea.  It is hard to find cabinet grade ply where I am, so I have been playing with the Sandi Ply from Lowes.  

For this practice set, I will cover with shellac and repaint.  

For the real ones I will use Maple for rails and styles, so maybe I don't have this issue.

For the door panels and the drawer fronts, I hope to find some cabinet grade 1/2 and 1/4 inch ply, if not the Sandi ply and figure out a why to smooth the panels. 

I have one more practice cabinet to build before I start the real ones.

Thanks Mike

You might want to use Targets HSF5000 with additional filler added. For poplar I use Gork’s “Goodfilla” spread on the surface with a rubber squeeze. Allow to dry and then sand. 
If memory serves, a blog post on Target’s site had a whole write up on using filler. Poplar is notorious for telegraphing its grain through the finish, both oil modified and waterborne. Particularly if the surface is painted. I try to avoid using wide  flat sawn pieces in door stiles, rails and casing pieces if possible if they are being painted. 
Ed

@Ed morini  

I switched to Maple to make them from.  I was hoping to save some money by using poplar, but was voted down by my wife when she saw how they looked painted.  I did another set using shellac first, and it came out a lot better, but I am thinking just use maple and be done with it.

I use the TC HSF on the plywood the sides are made of then sand a bit, I then paint them white on the inside with TC EM6600

Thanks
Mike

Mike L wrote:

I use the TC HSF on the plywood the sides are made of then sand a bit, I then paint them white on the inside with TC EM6600

Thanks
Mike

Mike
I have no direct experience with poplar, but I expect if you use TC primer - high solids - which you seem to have, that would go a long way towards leveling the surface.  Sand, 2nd coat HSF.  Once that is in place the top coat will be easy.  Just my expectation - have experience with these TC products, just not on poplar.  Also do check in with Jeff Weiss at TC - he does answer queries submitted to him.  I know, he did for me.

Henry