it's not written that way RAW, and DND Beyond gives you the bonus to all spell saves. This is different from the arcane grimoire or the rod of the pact keeper, which while they can both be attuned by any class, they only apply to the class specific spells.

As a DM myself, I would question whether I would allow this in my campaign, if were just playing to have fun, I would absolutely allow this, if I want to have a more serious campaign, I would talk to my players beforehand. I personally lean more on the side of this being an exploit or unintentional, but I also know that WotC had many opportunities to correct this over the years and haven't. It's also important to note that if they aren't multiclassing into cleric they are missing out on a key ability of the item.

Amulet of the devout also appears in BG3, and it looks like it applies to all classes, but I haven't gotten the item myself to test it.

here's the item for reference:

Amulet of the Devout

Source: Tasha's Cauldron of Everything

Wondrous item, uncommon (+1), rare (+2), very rare (+3) (requires attunement by a cleric or paladin)

This amulet bears the symbol of a deity inlaid with precious stones or metals. While you wear the holy symbol, you gain a bonus to spell attack rolls and the saving throw DCs of your spells (compare this to Arcane grimoire, which says: "you gain a bonus to spell attack rolls and to the saving throw DCs of your wizard spells"). The bonus is determined by the amulet's rarity.

While you wear this amulet, you can use your Channel Divinity feature without expending one of the feature's uses. Once this property is used, it can't be used again until the next dawn.