Use a glaze, not a stain.

The good thing is that the beams will be on the ceiling and not next to the floors, so if you get it close enough, it would be hard to really notice. We stained our beams the same color as the floor, but as the floors were white oak and the beams were something else, the beams ended up little darker and more solid color vs the floors that had a bit more variation. It doesn't "match" 100%, but it coordinates well.

It would help if we knew what all the samples in your photo were, but I think the above advice is probably what you need.

Better you read from a knowledgeable vendor.

https://itascawoodproducts.com/douglas-fir-stain/

It is too bad that you can't change the flooring...a bit of driftwood look for your scheme.

What are you painting the walls, and, most importantly, the trim and ceilings?

Here is a 5 year old post...may help you.

https://www.houzz.com/discussions/5468685/need-help-with-douglas-fir-timber-stain-color

" and didn't realize that the beams they were putting in are Douglas Fir "

Which wood shown is Doug Fir as I do not see anything I believe to be Doug Fir.

You cannot use the same stain for interior and exterior. That's now how wood finishing works. You are better off doing zero stain on the beams at all. Just the appropriate clear coat. But doug fir on the exterior isn't going to as long lived as you hoped without a lot more maintenance than you may have thought you were signing up for. Fake wood is much better than real wood for a lot of things, even though it costs more.

It doesn't have to be an exact match. You just need some of the tones of the floor to show up on the beams. I have engineered European oak floors, radiata pine boxed ceiling beams and on the lanai I have a cypress plank ceiling. They all complement each other. I worked with the painters to come up with the perfect product, colors and application methods to get the right colors for the beams and planks.

Thank you for all your comments. Both wood samples are douglas fir. The beige sample is the kitchen cabnets. Black is the exterior and they are all laying on a sample of the flooring. Walls and trim are going to be an off white with a ceiling white. Doors to rooms will have to be painted, since we cant find a stain. The problem is the front door, trim outside and beams. It would have been nice if the builder and architect would have told us about this wood before we picked out everything else, but it us what it is. So we are trying to figure out our options.

The flooring can probably still be returned. Most things can, unless they have been installed ... of course there will most likely be a substantial re-stocking fee, but I would assume you plan on living in this house for many years. So how much is it worth to you to have every element match perfectly if that is the one element you could still change?

You have what is cacalled gluelams. Laminated wood. It is what is needed to span the distance and hold up the roof. It's structural. The only alternative is steel. It is your builders only choice. So don't blame them. If it was ours. I would use minwax golden oak to pull the natural colors of the wood out and put varathane topcoat on them. Highlight them. Or you could wrap them in any wood you want to. Or sheetrock and paint. Possibly use wood flooring.

You could use steel on them painted black to accent the wood making them look more structural. Your builders are using standard building materials. And you have other options