"If you wanted a fence for the yard, there," he says, talking through lips partly closed over his pipestem, "and asked a plumber to build it, he'd make it out of pipe and couplings. If you asked a carpenter to build it, he'd use wood and nails. Give the job to a blacksmith, and he'd probably weld it, and a bricklayer would use mortar."
"It's a good idea to have a man around who is interested in none of these special arts, but is interested in the fence."
-Dick Dilworth, as recounted by Franklin M. Reck
And thus, the dentist you want is the sort who is interested in your teeth, not in any particular method of treating them.
Broken tooth? A crown is often the appropriate treatment, but onlays or even adhesive composite resins can be better in some cases.
Missing teeth? Implants, bridges or removable appliances are all ways to replace them.
Crowded, uneven teeth? There is a role for orthodontics with brackets and wires and a role for Invisalign, the tray-based system. Though some situations are definitely best treated with conventional braces. That's the thing--a dentist who tries to do everything with Invisalign is like the mason who only believes in fences made from bricks.
It's all about the fence. Not the biases of the person being asked to build it.