Nate Nagel wrote:

Wondering which would be more efficient in this situation...

A/C is set at 76 degrees. Dehumidifier is set at 55% RH. it's 67
degrees outside, approximately, but the house is right at 76 because it
was hot yesterday. Outside RH is 80+ percent.

Is it more energy efficient to open all the windows and turn on a fan,
and let the outside air cool the house off (thus forcing the
dehumidifier to run,) or just leave the windows shut at let the A/C do
its thing?

no, this isn't actually a hypothetical... this is exactly what I woke
up to this AM. I chose to open the windows because I like fresh air,
but on reflection didn't know which was really more efficient.

The enthalpy of the inside air is about 29.8 btu/lb. So, in theory,
you're better off opening the windows as long as the enthalpy of the
outside air is less than that.

For 67 degree outside air, the psychrometric calculator says that as
long as the outside RH is less than 89%, the outside air is "better."

In reality, there are a number of factors which will affect your
actual comfort, many of which have been pointed out. So, you'll just
have to try it and see.