Neil Martin, 29, appeared before Knowsley magistrates in Huyton, Merseyside, charged with racially aggravated harassment and stirring up racial hatred. The latter offence carries a maximum sentence of seven years imprisonment.
Martin, an office worker from Maghull, Merseyside, is alleged to have posted the comments last August, just days after 18-year-old Anthony was slain with an ice axe.
Dressed in a blue shirt and grey suit and tie, Martin did not enter any pleas and spoke only to give personal details.
The case was adjourned to Liverpool Crown Court for a plea and case management hearing on June 27. Martin was granted conditional bail.
The short hearing was attended by Anthony's mother and sister, Gee and Dominique Walker