Context. Direct observation of gamma-ray emission from the decay of $^{18}$F ejected in classical nova outbursts remains a major focus of the nuclear astrophysics community. However, modeling the abundance of ejected $^{18}$F, and thus the predicted detectability distance of a gamma-ray signal near 511 keV emitted from these transient thermonuclear episodes, is hampered by significant uncertainties in our knowledge of the key $^{18}$F(p,$alpha$) reaction rate. Aims. We analyze uncertainties in the most recent nuclear physics experimental results employed to calculate the $^{18}$F(p,$alpha$) reaction rate. Our goal is to determine which uncertainties have the most profound influence on the predicted abundance of $^{18}$F ejected from novae, in order to guide future experimental works. Methods. We calculated a wide range of $^{18}$F(p,$alpha$) reaction rates using R-Matrix formalism, allowing us to take into account all interference effects. Using a selection of 16 evenly-spaced rates over the full range, we performed 16 new hydrodynamic nova simulations. Results. We performed one of the most thorough theoretical studies of the impact of the $^{18}$F(p,$alpha$) reaction in classical novae to date. The $^{18}$F(p,$alpha$) rate remains highly uncertain at nova temperatures, resulting in a factor ~10 uncertainty in the predicted abundance of $^{18}$F ejected from nova explosions. We also found that the abundance of $^{18}$F may be strongly correlated with that of $^{19}$F. Conclusions. Despite numerous nuclear physics uncertainties affecting the $^{18}$F(p,$alpha$) reaction rate, which are dominated by unknown interference signs between 1/2$^+$ and 3/2$^+$ resonances, future experimental work should focus on firmly and precisely determining the directly measurable quantum properties of the subthreshold states in the compound nucleus $^{19}$Ne near 6.13 and 6.29 MeV.
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