How important is Load Shifting in MicroGrids?

From a revenue perspective, demand side management programs are perfect for a microgrid because it is able to island itself from the traditional synchronous grid.  I would expect that the majority would be participating in demand response programs simply for the reason that they are able to remove themselves from the traditional grid almost instantaneously while not interrupting much of their processes.  By participating in demand response programs, they can create an additional source of revenue while continuing to operate their facility at or near normal due to the islanding capability.

A lot to unpack here.  One meta question is "what is the purpose of the proposed microgrid?"  

DSM is ultimately a package of products and strategies targeted at different user and utility use cases; from this perspective, I think that prioritization of functionality depends upon value that can be derived...and the value depends upon the use case.  

A utility centric microgrid would prioritize DSM in response to the system needs that you've highlighted; a customer centric (i.e. MUSH, or residential "island") microgrid would prioritize DSM that balanced local reliability with the possibility of utility DSM revenue.  Either way - load shifting is a priority....but the right strategy behind the shifting will be different across different microgrids.  

Microgrids are just a microcosm of the “Grid” as the name suggests. The key difference being a lot more control both in developing forecasts and also insights into the load and supply sides when designing and managing the Microgrids. However, over time the peak shifting may be needed with variability and growth in the loads beyond the designed capacity or for managing supply side related events such as unplanned outages.

The backbone technology of most modern microgrids are photovoltaic (PV) power and battery energy storage system. Normally PV is used to charge the BESS during mid-day, and then BESS becomes the primary internal source at night  BESS has a very high capital cost, and there are two ways to minimize the size of the BESS: (1) use the BESS in the early evening, and utility power in the late evening (when utility power is usually least expensive), and (2) load shifting. However the load shifting may be the opposite of normal load shifting.

The least expensive power for a microgrid is generally PV (at least where I live in California).  So the load shifting would involve building larger PV arrays and shift flexible loads to mid-day when PV is generating at maximum output.

In order to provide an incentive this behavior, the microgrid manager would use an inverted  time-of-use rate, where consumer power is least expensive in mid-day and most expensive at night.

Load shifting is essential in a microgrid because it allows for the most efficient use of the resource. While a site is connected to the grid, the primary concern is typically energy management geared toward economic optimization (peak shaving, time of use, …). However, when islanding, power stability becomes a central focus and load management takes on increased importance, especially if the loads are being served by a battery system or other inverter based asset like a microturbine CHP for example. Sometimes loads just happen to occur at the same time, this doesn’t mean they have to.  Controlling and shifting loads, along with minimizing them through efficiency measures, enable microgrids to reliably serve their loads, take advantage of intermittent resources, like solar plus storage, and minimize the reliance on fossil generation in the microgrid.