Screen protectors are a standard accessory for new phones, but foldables are a different case. According to Engadget, it is fine to put a protector on a foldable phone's outer screen, which is essentially a regular glass display. The inner screen, however, is made of flexible layers and usually comes with a factory-installed protector. Applying an unofficial protector there can damage the entire display, so the advice is to avoid it.
Samsung's Galaxy Z Fold8 uses a TPU screen protector on its inner display, while Apple's iPhone Duo includes one with a nano-texture coating that reduces crease visibility. Both companies offer replacements for these built-in protectors, but only through authorized repair centers. The source notes that Samsung previously warned consumers not to remove the inner protector themselves after early Galaxy Fold displays malfunctioned.
Dust may be a bigger threat than scratches. The latest Galaxy Z Fold devices are IP48-certified, meaning they resist water and particles larger than 1mm but are not fully sealed. The iPhone Duo is IP68-certified and dust-tight, though that resistance is not permanent. For most foldables, a case that covers the hinge is a better investment than an inner-screen protector.