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is there any wood filler that will take stain like wood? or is there a stain or poly that will not discolor the filler?
which came first, the chicken or the egg?
There are fillers that take stain, but they will probably "show" the stain differently than the surrounding wood. To resolve that, you may need to mix a different stain shade with the filler than you would use on the wood to get a good match. Mix the stain with the filler prior to filling the screw holes. A little trial and error in a closet while taking notes on the mixture amount is the best way to tell.
The easiest thing to do is stain the floor and put on your first coat of finish. Then match your filler to that before your second cot of finish. But if you are filling holes I would go with plugs rather than filler.
Have you tried mixing your own filler? Take the sawdust from the same wood you are using and mix it with some glue. Then fill a hole on a scrap piece of the the same wood and stain it. If the mixture is correct (not too much glue), it should stain the same as the wood. Again, make sure the wood, sawdust and test piece of wood are all the same, good luck.
It will depend on what you're doing, how you go about filling and staining. Keep in mind that no matter what method you use, you're going to see the filled spot, so the best way to go about it is to avoid surface fasteners altogether. Barring that, Dap makes a very nice filler that is stainable called Plastic Wood. Dap also makes a "crayon" called Blend Sticks. A third putty option is Color Putty, which can be mixed with one another to create custom colors that will be almost invisible.
Putties and fillers have their place, but because they are made of a different material and density, they will never completely disappear. A better means of hiding larger fasteners is to use plugs. Plug cutters are inexpensive and allow you to use the same species of wood with the added benefit of matching graining. Plugs are more work, certainly, but will provide the next best thing to invisibility.
If you want truly invisible, you go with hidden fasteners, such as blind nailing, dowels, splines, pocket screws, or biscuit joints.
I'd go with blind nails above all else. They'll be out of sight and not need any fillers. Plugs would be a lot of work and unless you get really really lucky, they're going to show, depending on the grain of the wood. I use a piece of the same board to make my plugs just to try my best to get an "invisible" plug but you can only do it so many times.
Besides, making the plugs would require a drill press for safety and ease, in addition to a sharp Forstner bit to cut the recesses for the plugs. I'm too lazy to do that on just a floor. On my furniture, I'll go the extra mile. Go experiment with mixing your own colored filler and you might be happy. Make 2 or 3 different colors if you have a lot of holes because you'll run into varying shades of the wood you're trying to match.