The massive elliptical galaxy M87 has been the subject of several supermassive black hole mass measurements from stellar dynamics, gas dynamics, and recently the black hole shadow by the Event Horizon Telescope. This uniquely positions M87 as a benchmark for alternative black hole mass determination methods. Here, we use stellar kinematics extracted from integral-field spectroscopy observations with adaptive optics using Multi Unit Spectroscopic Explorer (MUSE) and Optically Adaptive System for Imaging Spectroscopy (OASIS). We exploit our high-resolution integral field spectroscopy to spectrally decompose the central actice galactic nuclei (AGNs) from the stars. We derive an accurate inner stellar-density profile and find it is flatter than previously assumed. We also use the spectrally extracted AGNs as a reference to accurately determine the observed MUSE and OASIS AO PSF. We then perform Jeans anisotropic modelling, with a new flexible spatially variable anisotropy, and measure the anisotropy profile, stellar mass-to-light variations, inner dark matter fraction, and black hole mass. Our preferred black hole mass is M_BH = (8.7 ± 1.2[random] ± 1.3[systematic]) × 10⁹ M_⊙. However, using the inner stellar density from previous studies, we find a preferred black hole mass of ⁠M_BH = (5.5^+0.5_−0.3) × 10⁹ M_⊙, consistent with previous work. We find that this is the primary cause of the difference between our results and previous work, in addition to smaller contributions due to kinematics and modelling method. We conduct numerous systematic tests of the kinematics and model assumptions and conclude that uncertainties in the black hole mass of M87 from previous determinations may have been underestimated and further analyses are needed.