McNulty grew up in Phoenix, Arizona and enjoyed riding mountain bikes in his free time with his father and his best friends, David, Ken, and Lance. McNulty excelled from early on, winning almost every mountain bike race he entered while racing in the 11-12 junior categories. McNulty gradually transitioned to road racing. After several wins in local races in Belgium in 2014, McNulty caught the eye of Bo Knickman, manager of LUX cycling. Knickman, realizing McNulty's talent, referred McNulty to coach Barney King. 2015 was a breakout year for McNulty, in which he won the Valley of the SunStage Race TT, averaging 30 mph on a standard road bike. McNulty won the junior national time trial championships that year and went on to compete at the UCI world championships in Richmond. In 2016, McNulty had even more success, winning the Tour de l'Abitibi and Trofeo Karlsberg, stage races, and the junior national time trial championships for the second year in a row. He also again competed at the UCI Road World Championships, and became the fourth American to ever become a junior world champion after Taylor Phinney, Jeff Evanshine, and Greg LeMond, winning the time trial by 35 seconds.
Professional career
McNulty turned professional in 2017, and despite being offered numerous contracts with UCI WorldTeams, he chose to ride with the AmericanUCI Continental team. He won the under-23 national time trial championships and finished second in the World Championships that year. In 2018, McNulty continued to ride with, who upgraded to UCI Professional Continental status that year. McNulty made his UCI World Tour debut in the Tour of California, where he finished fourth on stage 6, the queen stage, and ultimately seventh overall, about three-and-a-half minutes behind winner Egan Bernal. He would head to Europe for the second part of the season, after finishing 3rd overall at Tour Alsace, McNulty would have a string of good results at his first Tour de l'Avenir where he would finish 2nd on a mountain stage to Colombian rider Iván Sosa, demonstrating his ability on the climbs. At the UCI Road World Championships, McNulty would go on to finish 7th in the individual time trial event. In 2019, McNulty scored his first win as a professional at the newly revived Giro di Sicilia by winning the penultimate stage to Ragusa, and simultaneously taking the lead in the general classification. On the following day's fourth and final stage with a finish on Mount Etna, he managed to defend his leadership finishing 4th, thereby winning the general classification.