Time to quote Mark Twain:
"There are three kinds of lies; lies, damn lies, and statistics."
>>The $64,000 question is this: where are they getting these numbers<<
Parish registration, for certain. Doesn't mean they go to church every week, but does mean they probably at least go for Christmas and Easter.
>> Secondly: are they counting all the illegal aliens from Central & South America who are overwhelmingly Catholic? <<
Not sure, but possibly. Certainly, immigration is fueling the growth in the numbers of Catholics. Most of the largest sources of immigrants certainly are nominally Catholic nations (Mexico, etc.), but some are very irreligious (Mexico, Central America, etc.) while others are very devout (the Philippines).
I have a friend just back from Honduras who reports that no-one in Tegulcipada was even familiar with the concept of a marriage, so I imagine immigrants from such places don't remain identified as Catholics very long.
In eastern Somerville, MA, the population is at least 70% Hispanic and Brazilian; but the Catholic Church is devoid of any worshippers. The only Christian influences are a few store-front Pentecostalist churches.
On Long Island, most of the Hispanic population is Puerto Rican; they tend to at least maintain ties to Church.
From what I hear, LA Chicanos are mostly Marxist with only peripheral cultural ties to the Catholic Church, while in Texas, although the churches themselves are polluted by a dominant liberation theology, the Tex-Mexes are still more faithful. (These would seem to be the Bush Hispanics?)
In my present parish, attendance is very poor, considering the large number of Hispanics. (The area is 50% Hispanic, and only 20% of Anglos are Catholic, yet the Spanish mass has room to sit, and the four English masses are SRO.) The response is of course to condescend, so the Spanish masses are a three-ring circus.
>> American citizens who are Catholic are contracepting, aborting, and sodomizing themselves to death in the sense that they now have a low birthrate. The ongoing nonsense in the church inspires most of them to stay home on Sunday, not contribute....much less do the young in any serious number want to commit their lives to the church as priests of religious.<<
That definitely aptly describes Boston, but not red-state Catholics.
I know that when our parish is contacted we use the list of registered members. We update constantly and purge the roles of the people who have moved so we have a pretty accurate system. They don't all attend Mass every week and we have a lot who aren't registered in the parish but attend Mass regularly.
Just 37% of Hispanics are registered Catholics (thus, about 14 million of them, or about 20% of all Catholics). Your perceptions are not congruent with reality.
Without registration, no baptisms or Church weddings or first communions or funerals, so the number is pretty accurate.
The number of registered Catholics in parishes in Hispanic neighborhoods in major cities bears out this assesment.