This isn't an easy job no matter which way it's tackled. Well, unless you paint.
That godawful yellow/orange shiny finish is almost certainly varnish. Varnishes slowly yellow over time, but note that the pine itself will be part of it as the wood darkens slightly, and usually yellows, with exposure to light. Some subspecies of pine are also very notably yellow, much more so than the very white pine commonly sold in home centres today.
Depending on the age of your house and the time since the last refinish the varnish may also be what's called "gel stain" (thickened varnish with colour added) which could have actually been at that colour strait from the can, to immediately give the honey-yellow associated with old T&G pine panelling. I hate it too but some people love that colour!
So anyway, I think your options are strip, scrape or sand to get back to bare wood, or paint.
Chemical strippers are an excellent way to remove old finishes and often to be preferred over other methods. But if there's a large amount of wood to deal with stripping in situ could be an absolute nightmare job. Not just because of the amount of work but because you're dealing with a vertical surface, which is traditionally challenging to strip. And not least because this is inside rooms in your home, where you don't want to be using lots of chemicals — the fumes will spread throughout the house to some degree, especially if you have central air.
In addition the sheer volume of stripper necessary for a large job can be far more than you'd anticipate. For the panelling in a single room it might take two applications on every surface and that could mean three or four cans just for that one room. Multiply up for however many rooms you have to do.
In addition, you need — this is not optional unless you want to poison yourselves — solvent-rated respirators (these aren't cheap) for everyone doing the work or in the room while it's being done, eye shields, suitable rubber or nitrile gloves with long cuffs preferrably, drop cloths, multiple brushes, scraping tools or scrubbing pads, loads of wiping cloths or paper towels and a few other bits and pieces. And once you're done stripping the wood needs to be rinsed down and will likely need a light sanding to prepare it, so you're doing some sanding as well.
There is also heat stripping which has fallen out of favour in recent years. It requires a heat gun or blowtorch, scrapers, heavy gloves and eye protection. Wearing a respirator can be advisable doing this as well. Localised scorching of the wood is a constant risk with this method so it's often advised not to do in except when painting.
Homeowners don't scrape old finishes much any more but pros often prefer it where appropriate because of its efficiency and cheapness — no sanding materials to purchase, no chemicals, just one or two scrapers and the means to sharpen them. So it's very cheap. But it does require physical effort.
Large flat surfaces are the main thing where scraping is an excellent choice, at least technically. But again because of the size of the job and that these are vertical surfaces it would be a very demanding job physically. I would normally prefer this and would be recommending it but for these factors.
Sanding you shouldn't even consider IMO. But many people have done this sort of thing by sanding in this era of power sanders and will continue to do so. However, not only is it still far more work than people expect you're converting that varnish into dust and no matter how good the dust extraction on the sander some of it will escape. And fine sanding dusts can end up everywhere, and take days or weeks to fully clean up. In the meantime you'll be breathing some of it in. This isn't a desirable prospect just in a workshop, far less so in the home you live in.
Obviously you could paint over them as you've done elsewhere. This doesn't have to be a single uniform colour if you want, there are many other possibilities, I know you don't want to paint in these rooms but this may end up looking like the most attractive option because it would probably the least work by far, unless you...
Pay someone to do the work for you
This may be one case when paying someone for their effort is well worth it!
If you want to do the work yourselves there is one other option I would consider. I'm not comfortable putting this as the solution but I think it could be the best bet with a large amount of tongue and groove to deal with, ready? *gulp* Take down and deal with elsewhere. So you'd uninstall them (carefully!), strip them* or scrape them (much easier to scrape boards when they're horizontal) and then refinish and finally reinstall. It's a big job no matter how you look at it but arguably it's the best way if you want to retain the existing wood.
There is a final option I don't want to even mention but for completeness I have to include it..... rip out and replace. This is terribly wasteful of course but as awful as it sounds many times it's cheaper than keeping the existing boards, either in money or time or effort or all three. So if you do the math it can make the most sense economically. This is why this route would often be the one chosen by contractors if they aren't overpainting.
*In the garden or the garage or on the driveway. Or, have them stripped professionally but there's a risk here that the boards could warp from the process and there's no comeback.