CRJ-700 Captain reported erratic glide slope indications during approach resulted in an unstable approach and a low altitude alert from ATC.

Narrative

At 1;500 ft AGL just inside of the final approach fix; an aircraft on the ground crossed the approach end of the runway through the ILS critical area. ATC was utilizing ILS approaches to XXC in VMC conditions. As the aircraft crossed through the critical area; the ILS glideslope became erratic and dropped down multiple degrees of deviation. The Autopilot was engaged and attempted to track the glideslope; causing a sudden pitch downward while tracking the localizer. The descent rate reached around 1500 FPM down from what I recall.I advised that the pilot flying disconnect the Autopilot and continue handflying the approach visually. The pilot flying disconnected promptly and began to correct the transient altitude deviation. Still cross-referencing the inaccurate glideslope; the first officer took a moment to correct the pitch to an appropriate approach attitude. I stated 'pitch' and told the pilot flying to rely on the outside references again. At this time I turned off the flight director as well; to prevent further inaccurate information from the glideslope. While correcting the aggressive pitch down; ATC advised us of a low altitude alert and told us to check our altimeter. I replied 'roger'; and the altimeters were set properly. At this time we were regaining a stable approach path.Upon reaching 1;000 ft AGL; the pilot flying had stabilized the approach and met all stabilized approach criteria for a visual approach. He called 'one thousand' and I replied 'stabilized; cleared to land.' The approach and landing continued with no further issuesA key factor in this event was the automation becoming unreliable as an aircraft crossed through the ILS critical area. While ATC was advertising and clearing aircraft for the ILS approach to XXC in VMC conditions; they continued to cross aircraft at the approach end of the runway. This created the interference with the ILS that caused us to suddenly pitch down.Additionally; this was the first time that the pilot flying experienced an automation anomaly on approach; which may have affected the time taken to correct to the appropriate glide path from the transient nose down attitude. Once the pilot flying began using outside references; the approach stabilized and returned to normal quickly.Had a visual approach clearance been received; we may have been more likely to remain in GPS mode on the FMS and descended with VS mode on the autopilot; but due to the ILS clearance we chose to fly in green needles with approach mode. Since the conditions were VMC; ATC felt comfortable crossing aircraft through the critical area of an active ILS. Had they chosen to taxi the aircraft further down to Taxiway 1; the taxiway that we were advised to hold short of; the glideslope anomaly would not have occurred. With how busy ZZZ has been lately; it is not surprising that they would try to move an aircraft across the approach end of the runway in these conditions. As a crew; the transient state was corrected in time to meet the stabilized approach criteria; but we could also have chosen to go around due to the surprising nature of the Autopilot pitching down aggressively.