It comes down to one of two consistent positions:
1) The Newtonian model, in which a force is a frame invariant interaction
between objects. The net force on an object is correlated to its
acceleration as viewed from an inertial frame. Non inertial observers will
see "inertial effects" which, because of their own (the observer's)
acceleration, will mimic the accelerations produced by real forces.
2) The Einsteinian model, in which the concepts of both gravitational and
inertial forces are replaced by geodesic travel through non-Euclidean
space-time. The force concept is left to apply only to
non-gravitational/inertial effects (eg. electromagnetic interactions), which
are not (yet?) accommodated by this model.
The concept "real centrifugal force" has no place in either scheme. It
adopts the Newtonian word "force", but violates the Newtonian concept
"force". It is born of a subconscious desire to invoke a real force to
account for any and all accelerations - observed by any and all observers.
It makes frame dependent acceleration (as viewed by ANYONE) the definition
of force. This is neither Newtonian nor Einsteinian. It should drive a
thinking student wild!