This is an interesting subject.  There is a general public impression, I
think, that museum people have unhurried, relatively stress-free jobs.
For years, in establishing salary levels the State personnel folks gave
museum workers short shrift, for that reason.  I recall observing that toll
booth attendants who need only minimal qualifications to get jobs, were
making more money than well-educated and effective historical interpreters.
The State's knee-jerk reply was astounding:  those toll booth attendants
work under a lot of stress while your folks enjoy their work.

In the non-profit arena, members of my own board have observed that we have
enjoyable work, and that needs to be a factor in whether to locally
competitive salaries.

I wonder which types of positions are the most stressful, and which are the
least stressful.

It's my hunch that most of the stress is borne by a CEO and those attached
to that office -- the ones responsible for fundraising, promotions and
marketing, etc., i.e., everything having to do with "making budget."
Typically the CEO has no one in whom to confide during periods of stress --
that's also true of college presidents and corporate types.  CEOs can't let
their guard down, they must carry the torch of optimism even when things
seem about to fall apart; and
But what about those keeping the galleries & grounds neat and clean,
security people, the ones needed to keep climate control and other systems
in good working order.  The front desk and gift shop staffers in times of
heavy visitation.

These are all stresses brought about by "external" factors over which the
person has no real control.  These staff members, and others, are expected
to be up to whatever challenge comes from the environment.   Lack of
control over one's own job has been proven to be one of the greatest of all
stress-inducers.   A vacation or other break doesn't really help all that
much; what's necessary is the ability to occasionally "tune out" the
uncontrollable, and spend time on one's own priorities.

Then there are the professionals who must live up to their own expectations
of what they should do, usually established by generally accepted museum
standards.  They tend to work with limited resources, sometimes the
pressure of deadlines, distractions, etc.  But their "core" responsibility
is to live up to their own expectations, and so IMHO they are the ones who
put pressure on themselves.  I doubt they can actually get real relief from
a vacation, either.