How close to a Restricted Area can a pilot be cleared to fly?
ATC will separate IFR traffic from active special-use airspace according to the separation minima prescribed in the 7110.65 9–3–2:

Vertical separation: 500 feet above or below a prohibited/restricted/warning/MOA/ATCAA/ALTRV area (1000 feet above or below, if above FL290).
Radar separation: 3 miles from the periphery of special-use airspace; or for specific areas that have been designated by management as not needing 3 miles, simply &quot;clear of&quot; the periphery.
Non-radar separation: On airways whose protected airspace does not overlap the special-use airspace. (Remember that Federal airways extend four or more miles from each side of the centerline.)

Note that VFR traffic are explicitly mentioned as not prohibited from flying through a transitional hazard area (a term I think is used in conjunction with spacecraft launch and reentry). It is also &quot;common knowledge&quot; that VFR aircraft may fly through an active MOA but not active R- or P-airspace; however I can't seem to find anything that says this explicitly. R- and P- airspace is discussed at 14 CFR 91.133, which does not mention MOAs.

Without knowing the specific situation you're talking about, my guess is that when the restricted area is hot the TRACON is withholding an approach clearance using that approach for all IFR aircraft whether IMC or VMC, and only permitting VFR practice approaches to use it.