Significant variations in MHD activity and fast-ion transport are observed in the DIII-D high-beta, steady-state hybrid discharges with a mixture of electron cyclotron (EC) waves and neutral beam injection (NBI). When electron cyclotron heating (ECH) or current drive (ECCD) is applied, Alfvén eigenmodes (AEs) are usually suppressed and replaced by low-frequency bursting modes. The analysis of a recently compiled database of hybrid discharges suggests that the change of the fast-ion pressure especially the perpendicular pressure is the main factor responsible for the instability transition although the transition in some discharges can also be explained by a slight drop of the safety factor . The lower ratio of fast-ion injection speed vinj to Alfvén speed valfven and slight drop of during ECCD also facilitate the transition. The database shows that AEs mainly occur when the fast-ion fraction is less than 0.53 and is greater than 0.50, while low-frequency bursting modes appear in the opposite regime. Here, Pf and Ptotal are the central fast-ion pressure from classical prediction and total plasma pressure, respectively. The correlation with is weaker, and is around unity in all the cases. The reason why the instability transition correlates with and is that they can significantly modify the drive of low-frequency bursting modes and AEs. The explanation is supported by the observation that low-frequency bursting modes are rarely seen in the hybrids with NBI only, with EC waves and counter-NBI, or with high plasma density. A careful check of the low-frequency bursting modes suggests that they are mainly chirping (neoclassical) tearing modes (referred to as chirping (N)TMs), i.e. the mode frequency firstly jumps up from the steady (N)TM frequency, then chirps down, and finally returns to the steady (N)TM frequency. Occasionally, the (N)TMs are fully stabilized and replaced with pure fishbones. The resonance condition calculation and 'Kick' model simulations suggest that (N)TMs and fishbones can interact through modification of the fast ion distribution in phase space, which influences the drive.