The problem is the type of wood you used. Rotary cut SPF plywood is cheap, but not designed to look awesome when it is stained. That said, there IS a way to make is still look nice, but it will be a bit involved.
Wood filler rarely stains out nicely, that's why you try to minimize its use...
First of all, the Minwax stain is cheap and full of wax (as the name suggests) which makes it easier for the average Joe to work with, but also negatively affects its performance in colour consistency and penetration.
A better product would be anything from Goudey Stains. Remember this for next time
To fix it you want to do 2 things: get deeper penetration of the stain, and then layer colour on top, which you're only going to get in 2 ways: layering with Polyshades (meh), or spraying with a tinted clear sealer or topcoat.
If it were in my shop, this is how I would proceed:
1. Wipe the entire surface with mineral spirits or methyl hydrate to clean off any oil/wax residue, then give the entire surface a light sanding.
2. Recoat the wood with a proper penetrating sealer from Goudey, let dry 1-2 hours.
3. Make a mixture of clear sealer with about 10% stain mixed in. This would be a lacquer-based spray, which would be applied in thin coats, slowly filling in the colour of the wood.
4. Once it dries, top coat it with whatever you want, lacquer, oil or latex. Just give the lacquer 24 hours to cure.
If you have the tools, it's not as hard as it sounds. I say this all so that you have an idea of how it would properly be done (apart from re-skinning it in a true stain-grade wood)
How you could simplify the process:
The problem with oil-based stains and urethanes is that they take so long to dry, making layering difficult at best. You'll need to lay the stand flat so each side can dry level, without any drips or runs, else you'll be upset at the results.
You can use Polyshades, or mix a bit of stain with a bit of clear polyurethane, and by putting it down in layers, you will darken it up evenly. But without being able to spray the layers, I don't know if you'll be happy with the results.
If you did it all with with latex stain, it would be easier, as it dries faster. But you'd still want to be able to spray it on.
Sorry it's not going to be easy....