I can only repeat this is not the right John. This is John James with mother Mary Ann.
The John in question is John Joseph with mother Catherine.
Do you hold a copy of the 1880 NSW BDM birth registration document for John James EVERITT? (# 2745)
Do you hold a copy of the 1880 NSW BDM death registration document for John J EVERETT? (#2720)
Is it NOT worth considering that as you are looking for a birth registration for your Wilfred Charles EVERITT, that you ought to be checking the actual records (as opposed to the INDEX) for any births registered in that surname, especially where there is NO father noted? It could well be that your Wilfred was born in 1880 rather than in 1881 ...... afterall you already have two possible birth dates (May and June 1881) .... and your John Joseph was summoned on Indecent Assault charges in April 1880, so the assault was prior to those charges .... so Wilfred/Charles/Robert/Bob may well have been born say May or June 1880, rather than 1881 .... perhaps John Joseph was indeed himself assaulted sometime after October 1880 (ie after being found by the court to be not guilty of indecent assault on Julia) ....
You need to aim to get as close as possible to original documents from that period. Official transcriptions of NSW BDM original bdm registration documents are the better option, as they are cheaper, and can be delivered by email attachment. So you can get more primary documents for your pennies. Then of course, you can attend NSW SRO and look up the various files they hold there, and read these for yourself, take copies etc.
But please try to avoid relying on information you find on INDEXES ... they are simply pointing you to THE RECORDS and are not of themselves a record to use to confirm or eliminate a possible 'fact' when you are looking for clues to a family history mystery in NSW rural districts, in the 1870s and 1880s.... (or in any other era for that matter !).
Cheers, JM