What would prohibit a T-38 Talon from being certified in the Acrobatic category?
That an aircraft is eligible for a category is not a basis to say that the aircraft should be certified in that category. In other words, though there is nothing prohibiting T-38 being certified in acrobatics category, FAA will not certify it unless someone approaches it for that reason.

The T-38 would come under military surplus aircraft, which is covered by FAA Advisory Circular 20-169 for Military and Special Mission Modifications and Equipment for Commercial Derivative Aircraft.

However, there are some T-38s being operated by civilians in US, which are type certified under FAA Experimental Category (most are used by NASA, Boeing etc for research). One of the aircraft owned by Thornton Corp. is certified under the 'Exhibition' category, which permits the user,


  to exhibit an aircraft’s flight capabilities, performance, or unusual characteristics for air shows, motion pictures, television, and similar productions, and for the maintenance of exhibition flight proficiency.


I'm not sure if this aircraft has been used in that manner though.