Is there any evidence of a Birth of James Keefe in Wexford in 1865

[ALAMO2008]

In January 1881 a James Matthew Keefe joined  the Royal Navy as 115510 Station his Birth as 22 October 1865 Liverpool

But in 1885 a James Keefe enlisted into the 21st Hussars aged 19 as 2450 stating Birth as Kilmore Quay Co Wexford

This has split the Ancestors whether he was born in Liverpool or Wexford in 1865 because not only means his Parents had different Names as well as the Birth Year.

I maintain he was born 22 October 1866 in Liverpool December Quarter 1866
but the Ancestors won't accept that because it gives a different Mother's Name not known to them.

To Solve it- Was there a James Keefe born in Wexford in 1865?

and if so -are his Parents Known?

His Father was named John Keefe or Keeffe a Tailor Journeyman
 who might have had a Wife previously
 and Daughter Margaret

[Milliepede]

What birthplace does he have on census?

James has parents and an older sister born Ireland in 1871

What do you mean by the ancestors won’t accept it as the mothers name is not known to them 

The birth registration for Liverpool will have mothers maiden name

[aghadowey]

I don't understand either-

What do you mean by the ancestors won’t accept it as the mothers name is not known to them 

The birth registration for Liverpool will have mothers maiden name

From GRO index-
KEEFE, JAMES  MATTHEW     MCGEORGE  [McGeorge being mother's maiden name]
GRO Reference: 1866  D Quarter in LIVERPOOL  Volume 08B  Page 154