Different schools handle selective majors differently. At the highly rejective schools where there are many more qualified applicants than room for students coaches seem to have some pull for selective majors, or at least selective colleges within the university. At a state school (for example), it is more likely the college has found a lower limit that is needed to be successful in the major and will let a student in if they meet the qualifications. The coaches at these schools are not likely (or able) to help a student get into a major they might not be qualified for, but many coaches will let a student athlete chose a major they can get themselves into.
There is variation from sport to sport, too. Many XC and swim programs have many engineering students on the team. Baseball? not so much–the travel for games gets in the way of classes and it usually just doesn’t work.
My son looked at a decent number of D1 and D3 programs for XC and TF. Every single coach we spoke with said they had no limits on what their student athletes could major in, and every program had student athletes majoring in engineering.