General aviation pilot reported an NMAC during approach with an aircraft on the same approach as directed by ATC. Reporter took evasive action to avoid a collision.

Narrative

While on a flight on Aircraft X today; around XA27; we had to make evasive maneuvers to avoid a collision with Aircraft Y. We saw their aircraft approaching rapidly from our 11 o'clock; and I (safety pilot) demanded a right climbing turn to the right to avoid.Two factors that I think helped contribute to this incident were the Tower (ZZZ) directing both aircraft to start their approach at the FAF of ZZZZZ; with both aircraft instructed to 'report crossing ZZZZZ.' Both aircraft were aiming to cross ZZZZZ at 1;800 ft; which caused them to come close to merging into each other.The second factor was a lack of situational awareness; with Aircraft Y not giving priority to the aircraft on its right as per 14 CFR 91.113; and also our own crew not noticing the possible collision earlier due to being focused on the approach procedure; leaving us with no option but to take evasive maneuvers.After reviewing a copy of the ATC recordings and analyzing the ADS-B data; we believe that the lack of advisories from the Tower and the lack of situational awareness from the airplanes involved were the two major factors driving the incident today.