FRB 180301 is one of the most actively repeating fast radio bursts (FRBs) that has shown polarization angle changes in its radio burst emission, an indication for their likely origin in the magnetosphere of a highly magnetized neutron star. We carried out a multiwavelength campaign with the FAST radio telescope and NICER X-ray observatory to investigate any possible X-ray emission temporally coincident with the bright radio bursts. The observations took place on 2021 March 4, 9 and 19. We detected five bright radio bursts with FAST, four of which were strictly simultaneous with the NICER observations. The peak flux density of the radio bursts ranged between 28 and 105 mJy, the burst fluence between 27 and 170 mJy ms, and the burst durations between 1.7 and 12.3 ms. The radio bursts from FRB 180301 exhibited a complex time domain structure, and subpulses were detected in individual bursts, with no significant circular polarization. The linear degree of polarization in the L band reduced significantly compared to the 2019 observations. We do not detect any X-ray emission in excess of the background during the 5, 10, 100 ms, 1 and 100 s time intervals at/around the radio-burst barycenter-corrected arrival times, at a > 5σ confidence level. The 5σ upper limits on the X-ray (a) persistent flux is <7.64 × 10-12 erg cm-2 s-1, equivalent to L X < 2.50 × 1045 erg s-1 and (b) 5 ms fluence is <2 × 10-11 erg cm-2, at the radio burst regions. Using the 5 ms X-ray fluence upper limit, we can estimate the radio efficiency η R/X ≡ L radio/L X-ray ≳ 10-8. The derived lower limit on η R/X is consistent with both magnetospheric models and synchrotron maser models involving relativistic shocks.