thanks for the reference, and I understand that many rites are recognized by the Catholic Church, and that is an official teaching.
but as it relates to baptism, is it an official teaching that a person is baptized into a particular rite?
As far as I know it is.
I've been looking this up and the best I can find so far is from the Catholic Answers Forum.
The question was posed "What’s the process of changing rites in the Church?"
That question and the answer implies that one is "in" a particular rite.
The whole answer is long but I'll post if for you anyway. Note the bit I have emboldened.
"Since sometime during the reign of Pope John Paul II it the term changing ‘rites’ is not quite appropriate.
When it was just one church with different rites that made sense, but today the various patricular ritual churches are regarded as Sui Iuris, or with it’s own law, and they are theoretically all equal before the Pope. Also, some of these Autonomous Ritual (Particular) Churches share the same liturgical tradition so one has to be specific as to which church a person is changing to. (For instance, the Ukrainian Greek Catholic church and the Romanian Greek Catholic church use the same liturgical tradition/ritual tradition, one does not join the liturgical tradition, one joins the church.)
Therefore, one does not change ‘rites’ as such, one changes churches. This is referred to as canonical enrollment, and although there are exceptions
the simple answer is one is normally automatically enrolled in the church of one’s father at baptism.
Changing canonical enrollment requires the agreement of one’s present bishop as well as the receiving bishop (they will usually be different dioceses with overlapping territory). If both bishops agree, the approval of the Holy See at Rome (which reserves the right to rule on this) can be assumed.
To do this one should have the pastor of the new parish (one can join a parish of another autonomous church without actually changing canonical enrollment) help in writing the letter or letters. The pastor can help one know of the particular requirements the new bishop will place on the candidate. One should not wait for the pastor or missioner to suggest one transfer, he might never do so, for to suggest such a thing could be construed as poaching members from a sister church. He will probably be satisfied if the person enrolls in the parish and makes regular contributions.
Some receiving bishops will allow one to transfer into their care in less than a year, some will require an indefinite wait and I knew of one who required a three year period of participation and life on the new calendar. One’s former (or as it actually is, the present …) bishop may not approve if he thinks one is not a good Catholic (no prior parish registration or recorded contributions for instance), or that the reason one is leaving is to skirt canon law.
In some odd cases the church one wishes to transfer into does not actually have a bishop, because the Pope has not erected a diocese. One example could be the Russian Catholic church, which has no bishops (not even in Russia). In that case the local mission will probably be under the local Latin ordinary and if one is already a Latin Catholic living close enough it is conceivable that one’s new bishop will be the same as the old bishop!"