Marty Blagborough, 28,of Leeds, and Arthur Taylor, 61, of Wakefield, both appeared at York Magistrates' Court on Thursday afternoon.
Both men, along with Edward Warren, 60, from Leeds, are charged with obstructing a person who was engaged in lawful activity.
The men were arrested on Monday, January 11, following reports a group had attended the Poppleton Park testing site in York and were acting in an aggressive and threatening manner towards staff.
Blagborough and Taylor's case was adjourned until March 9, for further case management.
Warren, who was due to appear at the same court on Tuesday but could not attend due to the fact he is self-isolating with coronavirus symptoms, will appear in court again February 19.All three men were granted conditional bail and must not enter North Yorkshire except to attend their court hearings.