This is from memory so I can not document or source it but as I recall bleach can be harmful to the plastics used in the water system including but not limited to:
The Tank
The lines
The water pump
The fittings
And valve seals
In low doses (1/4 or even 1/2 cup per 15 gallons not much of a problem
But in high doses (Straight out of the bottle) and allowed to sit in the lines.. Major issues.
How to test.. You can easily get a few inches of PEX at your local RV place.. toss it in a glass glass or dish and cover with blach 100% strength. Come back in a day and see what it looks like.