Entropic gravity, as proposed by Verlinde in his original article, reproduces the Einstein field equations and, in a Newtonian approximation, a  potential for gravitational forces. Since its results do not differ from Newtonian gravity except in regions of extremely small gravitational fields, testing the theory with earth-based laboratory experiments does not appear feasible. Spacecraft-based experiments performed at Lagrangian points within our solar system would be expensive and challenging.
Even so, entropic gravity in its current form has been severely challenged on formal grounds. Matt Visser has shown that the attempt to model conservative forces in the general Newtonian case (i.e. for arbitrary potentials and an unlimited number of discrete masses) leads to unphysical requirements for the required entropy and involves an unnatural number of temperature baths of differing temperatures. Visser concludes:
For the derivation of Einsteins equations from an entropic gravity perspective, Tower Wang shows that the inclusion of energy-momentum conservation and cosmological homogeneity and isotropy requirements severely restricts a wide class of potential modifications of entropic gravity, some of which have been used to generalize entropic gravity beyond the singular case of an entropic model of Einsteins equations. Wang asserts that:
Cosmological observations using available technology can be used to test the theory. On the basis of lensing by the galaxy cluster Abell 1689, Nieuwenhuizen concludes that EG is strongly ruled out unless additional (dark) matter-like eV neutrinos is added. A team from Leiden Observatory statistically observing the lensing effect of gravitational fields at large distances from the centers of more than 33,000 galaxies found that those gravitational fields were consistent with Verlindes theory. Using conventional gravitational theory, the fields implied by these observations (as well as from measured galaxy rotation curves) could only be ascribed to a particular distribution of dark matter. In June 2017, a study by Princeton University researcher Kris Pardo asserted that Verlindes theory is inconsistent with the observed rotation velocities of dwarf galaxies.  Another theory of entropy based on geometric considerations (Quantitative Geometrical Thermodynamics, QGT) provides an entropic basis for the holographic principle and also offers another explanation for galaxy rotation curves as being due to the entropic influence of the central supermassive blackhole found in the center of a spiral galaxy.
In 2018, Zhi-Wei Wang and Samuel L. Braunstein showed that, while spacetime surfaces near black holes (called stretched horizons) do obey an analog of the first law of thermodynamics, ordinary spacetime surfaces — including holographic screens — generally do not, thus undermining the key thermodynamic assumption of the emergent gravity program.
In his 1964 lecture on the Relation of Mathematics and Physics, Richard Feynman describes a related theory for gravity where the gravitational force is explained due to an entropic force due to unspecified microscopic degrees of freedom. However, he immediately points out that the resulting theory cannot be correct as the fluctuation-dissipation theorem would also lead to friction which would slow down the motion of the planets which contradicts observations.