As it says, many classes have abilities that say "DC is your Spell DC." Which is fine but items that add to your spell DC are not applying to these abilities. 

For example: "Some Channel Divinity effects require saving throws. When you use such an effect from this class, the DC equals your cleric spell save DC." And my Light Domain cleric has an item that raises the Spell DC by one, making my Spell DC go from 16 to 17, yet the wording on the ability page of our characters sheet do not reflect this. Our Spells do, but not abilities are suppose to be based on that DC. 

We had a dispute on this in a game because DNDbeyond does not add it for the class abilities across multiple classes.

EDIT: My DM is saying supposedly someone from WoTC has said that spell increasing items do not increase class features. So really odd on the wording. And if this is true, some clarification would be nice. 

I think changing your channel divinity DC that it depends on the item specifically. What item is giving you the +1 to your spellcasting DC?

DM is using some homebrew items that give a +1 to dc.

I get the reason of saying "cleric spell DC" I had a Multiclassed Sorc/Cleric and since he wasn't raising his Wisdom then his "cleric spell DC" wasn't raising. But if an item raises your spell DC, should that not apply to Class features specially Spell-like abilities? 
I know TCE made new items and it is specific about being for Spells.

You cannot affect the DC of subclass features without homebrewing a copy of the subclass and adjusting it in the code, you cannot affect the DC of base class features at all.

I was thinking about the Amulet of the Devout which gives a plus to spell attacks and save DC and gives an extra use of channel divinity, not increasing its DC by one. So... What Sposta said.

Yeah, those Save DCs are just snippets, there’s no way to affect them except directly.