The church determines soeone is a part of the membership based upon baptism--once a Catholic, always a Catholic...even excommunications aren't calculated.
But there are some finite measurements that are known: the most significant (and alarming to Catholics) is the drastic decline in religion vocations that has now beyond a half century The average age of nuns in the US is in the normal retirement range. The number of priests is down sharply: in Eastern Iowa, as a close-to-home example, it is not unusual now for three or four parishes to share a priest, and priests in the larger parishes in the Davenport Diocese serve masses during the week in parishes for whom a fulltime paster is not available.
What we do know anecdotally is that despite the closing of many parish churches and fewer masses in many others, the pews are not nearly as filled as they were fifty years ago. And what we know from survey data is that both the percentage of Catholics who attend mass on a somewhat regular basis nad the number of Catholics who rate religion as seriously important in their lives has been declining for the past six decades.
The same is true for mainstream Protestant denominations and for Reformed & Conservative Judaism. As for pentecostal and fundamentalist Protestants, the picture is far from clear. It is obvious that the REligious Right continually inflates the number of adherents...and it is notorious that there is a sizable contingent of "the saved" who repeat the process very frequently, walk the sawdust trail to Redemption so long and so often their feet get blistered.
The inherent problem with ALL data about church membership and religious identity is that subjective devil of measurement termed "intensity"--and no one has yet been able to suggest a sensible objective standard to implement the intensity of commitment.
Of course none of this matters much as having any relevance to Notre Dame athletics. Not only are many of ND students not Catholic, the same is true of the faculty--including even the Depts of Religion & Philosophy (especially the latter). The long continuing decline of Notre Dame's fan base is evident even in its most traditional core, Chicago. Ironically, the primary reason is the rapid geometric rise in college attendance: ever since the end of World War 2 and the start of the GI Bill, the sons & daughters of working class families have gone to college instead of the stock yards, steel mills, etc--and become alumni of the Big Ten and other state/public universities instilling their sons & daughters as toddlers with a passion for dear old dad's college team--until they go elsewhere themselves. And not only is the last generation of "street-car NMD Irish" dying off, even their neighborhood bars are disappearing as well (less than a third as many of them now as thirty years ago with Mayor Daley determined to close down those that remain--while the "sports bars" on the Near North, Lincoln Park, "Wrigleyville" are packed with fans watching three different Big Ten games on separate screens simultaneously).