Why do some AFBs have planes parked at 45 degrees to others?
McGuire AFB being an Air Mobility Command (AMC) base, accounts for the very large C-5 Galaxy when it visits. It may not seem like it, but the 68 m (220 ft) wide C-5 when parked at a 45-degree angle saves ~20 m (65 ft) -- approx. one-third of its wingspan.
The reference used by the USAF is AFMAN 32-1084 (PDF), from which:

2.1.5.4.1. Parking Dimensions. Table 2.9 presents the minimum geometric criteria for fixed-wing apron design. When designing new aprons for AMC bases hosting C- 5, C-17, KC-10, and KC-135 aircraft, provide 15.3 m (50 ft) of wingtip separation.
EXCEPTION: When you are rehabilitating an existing apron, provide the maximum wingtip separation the existing apron size allows (up to 15.3 m [50 ft] but not less than 7.7 m [25 ft]). This additional separation is both desirable and permitted.

By applying that to the C-5 and adding the clearance to the taxiway, those angled spots are a perfect fit:

The measurement above (~83 m) shows two half-span C-5s (68 m) plus the clearance (15.3 m), with superimposed C-5s via pinterest.com

For the other examples you've stated in a comment: Beale AFB and Albuquerque Airport, Tinker AFB, and March AFB -- in that order:

The parking spots are between two taxiways, so it's the same reason as the main example. It also makes parking and taxiing out easier.

Those by the hangar are for ease of taxiing out instead of a hard left and potential for collision.

Plenty of space. I couldn't find a 45-degree parking.

(All imagery is via Google Earth)