Both are tools
Shoes protect and add traction. A barefoot trim lets the hoof wear and flex when the wall, sole, and the work agree with each other. Neither choice is a moral position. The question is whether this horse, on this footing, doing this job, stays sound.
A backyard horse on soft ground may do well barefoot with a steady trim. A horse that works on rock, that needs studs for a job, or that has a foot the farrier is supporting while something else heals, may need a shoe for a season or for good.
Barefoot still needs a person
Pulling shoes is not the end of the schedule. The hoof keeps growing. A hoof-care trimmer or a farrier who trims only should still come on a cycle, and the horse should be comfortable on the surfaces it actually lives on, not just in a soft round pen the day the shoes come off.
Hoof boots are the middle path a lot of horses use: barefoot in the field, booted for the rocky ride or the hard road. Boots are equipment you maintain. They do not replace the trim.
Shoes are not a failure
A shoe can be a reset, a keg shoe, or something shaped for a specific foot. Therapeutic shoeing belongs in a conversation with the farrier and, when the horse is lame, with a veterinarian. Do not ask a listing on a website to choose a package for a horse it has never seen.
If you switch from shod to barefoot, expect a transition. The sole and wall that lived under a shoe are not instantly the same as a hoof that has been working bare. Plan easier work, watch for tenderness, and keep the next appointment close.
What to ask
Ask whoever you hire what they see on the sole and the wall, not only whether they are 'a barefoot person' or 'a shoeing person.' A useful answer mentions this horse's feet and your footing. A useful farrier or trimmer will also say when the job is outside what they do.
Certifications, if a business lists them, are self-reported on this directory. Ask which organization issued them and check with that organization yourself if it matters to you.