Remember, they would be federalized Nation Guard ... not regular Army. They are citizen soldiers and I believe there would be a lot of units who would not fire on their fellow Americans. Yes, I know about Waco, but a lot has changed since then. They are never armed anymore in riot situations.
I believe many Governors would stand against their State Guards being used to kill those protecting their lives and families. It would be a huge mess. BTW, I didn't see the National Guard demanding the Koreans on their store roofs lay down their weapons during Rodney King riot.
If enough solid citizens organize (not screwball white supremacist militias) and started blocking towns, neighborhoods, streets against the hoards, I don't see any mass killing of regular Americans by the NG. However, I do see quite a few deaths and injuries to the zombies if they were dumb enough to move on the suburbs, especially if they just start killing whites (or anyone) at random. There would be a number of whites killed as in the scenario above, but then a thresh hold would be reached at certain point/number.
If the zombies only target individuals at malls and such, that alone would have a significant economic impact on the local economies. Not sure what could be done about that tactic if they hit and run - like the current hit and run beatings. Forgot what they're called. Like I said, it would be a political, economical, and social mess.
As for LEO, many will sick out to protect their own families. They did little to nothing during Rodney King. I watched the whole thing unfold from ground zero on day 1 until it stopped. My take as to why is the zombies just ran out of boozed, energy, places to burn. The NG presence probably had an affect, also.
but a lot has changed since then......Such as? Oh, yes. Obama.