Assume that the military rules broadly accord with those in the civil world (with Class D being a civil classification and all that

)
In which case, when dealing with unknown aircraft in Class D airspace the instructions to military ATC would be akin to:
Passing traffic information on unknown aircraft unless the primary function of sequencing and separating IFR flights is likely to be compromised.
If a pilot requests Avoiding Action it shall be provided to the extent decided by the radar controller.
Give Avoiding Action if radar derived or other information indicates that an aircraft is lost, has experienced a radio failure, or has made an unauthorised penetration of the airspace.
If the pilot decides not to comply with the Avoiding Action advice, he becomes responsible for his own separation and any Avoiding Action which may subsequently become necessary.
So, in BEagles case at point, and confirmed by rej, in terms of Avoiding Action it seems it is being carried out exactly as it should be. Unfortunately, if the JSP rules are the same as those we have in the civilian world then there is no leeway to
not pass information on unknown contacts (unless you use the defence of being too busy with IFR tasks as detailed above

). Perhaps it's one for the rulemakers to look at changing in respect of VFR traffic receiving a service. They should be looking out the window after all, admiring the trains, trucks, and tractors below !!