The impact of anisotropic pressure models in neutron stars (NSs) is increasing their compactness. Therefore, for the relatively soft NS equation of state (EOS), we can still obtain a relatively large maximum mass of NSs and a relatively short canonical NS radius. We systematically study the anisotropic NS properties using a refined EOS. We compare the results with the recent NS multimessenger constraints. We use a relativistic mean-field (RMF) model with the G3 parameter set to calculate the NS core EOSs. The standard SU(3) prescription and hyperon potential depths determine the hyperon coupling constants. We use the inner and outer crusts EOSs from Miyatsu et al. [Astrophys. J. 777, 4 (2013)AJLEEY0004-637X10.1088/0004-637X/777/1/4]. We consider two kinds of EOSs at high densities: one with the maximum speed of sound in NS matter obeying the conformal bound, i.e., vsmax=13 (WHSS) and one without considering this bound (WH). We have found for the WH EOS with Δ=-1.8 that NS properties predicted for an anisotropic NS based on the Horvat et al. model [Classical Quantum Gravity 28, 025009 (2011)CQGRDG0264-938110.1088/0264-9381/28/2/025009] are entirely compatible with recent NS multimessenger constraints. Whether a 2.6M⊙ massive compact object observed in the GW190814 event is an anisotropic NS or not, we found that the compact object is not likely an anisotropic NS.