I work with wood flooring. I have not stained hickory, but I am not surprised that folks find it resistant to penetrating stains, as the wood is dense. The only place on the boards that will accept pigment well will be the soft wood of the grain pattern. As a consequence, the floor will only become more busy-looking, because the staining will accentuate the grain pattern.

The problem that some people have with peeling of finish over stain has a lot to do with the finish not adhering to the pigment that rests on the wood after the vehicle (usually hydrocarbons) has evaporated. Unfortunately, stains do not include much in the formula that resembles a binder; little binder equals little sticking power. A piece of peeled finish will carry with it the pigment the finish was applied over; the pigment layer in such a case is the weak layer. Some stains include more binder than others. The stain I use almost exclusively is DriFast by Bona that I believe is a thin oil-modified urethane with pigment added. I have had no peeling issues whatsoever using that product in combination with their finish materials.

A wood floor finish expert will know about 'water popping' and sanding schedules that will prepare any wood for a proper staining.

Some of us in the industry have been experimenting with paint slurries as a staining media, especially where a very dark result is desired. It works, because of the binders in the paint film. However, anyone who attempts such a thing had better do the necessary testing to determine whether or not the chosen products work well as a floor finishing technique and are compatible.

There can be problems staining hickory. The biggest one for site finished floors is the every little sanding scratch not carefully orbited out will show up in the stain.

We use an extra sander and two additional steps in our process for staining hickory, maples and other smoother surfaced woods which share the same traits. Water popping being one of them.

I wish I could share photos with you of my brother's home. He put finish on site solid hickory throughout his whole house and just put a urethane finish on it.
I thought he was crazy. What a wild floor. Thought his bride to be (who was lived out of state at the time) would kill him with such a "loud" floor to decorate with? around?.
I am glad to say, it is fabulous the way it is. So much character. That with the furnishings in place, it really looks beautiful. I say, if you've got it, flaunt it. Don't be self conscious of its beauty. I bet it looks FABULOUS dahling.

We just got the same response from two refinishers. Both say they can't stain the floors dark because the variation in color will be too great and the floor won't look good.
The current hickory flooring is in the dining room/kitchen and are stained so they look like yellow pine. The dining room opens directly to the living room where the floor is a dark brown Saltillo tile. The contrast is shocking and we want to more closely match the dark in the tile.
If anyone has done this successfully, please post pictures or let us know how you did it. Thanks!

Many years ago I used aniline dye (water stain) on a very old hickory floor for a customer.

It cam out very well.

Water staining on floors seems to have disappeared completely though.
Unlike pigment stains that sit on the wood (and collect in any scratches present) aniline dye can be used to make wood more uniform in color if that is what you are after.

It can be affected by differences in water absorption of the wood, but using multiple coats of different strengths starting with the lighter color can work to uniform the wood up.

I have character grade Hickory with Waterlox on it. 3 coats of satin/sealer and 1 coat of satin finish, per Waterlox VP. Your cabinet door looks like it is hickory heart wood. Take a look at Waterlox website. Water popping can be tricky in order to get stain to take and be even. A clear coat of poly on character hickory will keep the sap/white pieces white, but poly will yellow--overtime. I will try and post my pic of floor. Waterlox put a nice warm glow to the sap of the hickory and wonderful dark of the heart wood.

The floor guys used Glitsa (a swedish floor finish) on our floors when we built in 2011. So far they have not yellowed.