Fr. Hesse's advice might be sound.  But it only makes sense in the context of a person who grew up in Catholicism at all.

Eastern liturgy is not the only issue when speaking on this topic. Addressing this a simply Eastern Rites is to look at this from an wholly Latin perspective, greatly distorting the matter. What is being discussed is eastern ritual CHURCHES, not merely different Rites. The Latin Church sui juris is unified in jurisdiction under the Papacy and has (today) very few rites, namely Roman, Ambrosian, Mozarabic, as well as some local usages. The Eastern Churches are 23 distinct Churches from the Latin Church which total collectively (all 24 Churches) comprise the communion that is the one, holy, catholic, and apostolic Church. 

Um...the Pope has universal jurisdiction -- over anyone calling themselves Catholic.

I honestly don't know about your question at the end.

I'll say this: I don't know if you told me where you're from, but between other things you've said ("all my daughters' friends wear makeup", hostility experienced towards large families, and speaking of a variety of Eastern Rites being in your area, I'm thinking you're not in Texas, much less rural Texas)

Even in the 2nd largest city in Abraham Lincoln's home state, the Eastern Rites were a complete non-issue my whole life. If there were any, then no one I know was aware of them or even mentioned them -- pro, con or anything in-between.

Yep, there's a HUGE variety of such things up here in the Cleveland area.  Cleveland was THE Eastern European melting pot in the U.S. for about 30-40 years.

Fr Hesse made the point that one should stick with the rite of Church that one grew up in.  Obviously, times are so that fulfillment of one's sunday obligation makes attending Eastern rites necessary but his/Matthew's points are similar in that a Western-born mindset would be attuned to the Latin rite, while a person born in the East would gravitate towards the Eastern rites, all things being equal.  I would think that some minor things in the West would be scandalous (at first) to an Eastern rite Catholic and vice versa.

Well, maybe, but the Church would readily allow people to switch Rites, primarily from Roman to Eastern, before Vatican II.  There was reluctance in letting Easterns go Roman because of the risk that the Eastern Rites would eventually be swallowed up into the much more populous Roman Rite.

It seems like a lot of you were born Latin Rite Catholic, which I assume would explain the whole "having to get approval to switch" thing.  But that wouldn't be relevant only for a person who had already converted.

What would be your thoughts on a Protestant *deciding* to convert to the Eastern Rite, as opposed to the Roman one?

The parish I go to is almost totally made up of Roman Rite refugees who have fled the Novus Ordo.  There are only two elderly members of the parish left, the rest of the fairly good size parish are all from the Roman Rite, from all sorts of ethnic backgrounds that are not Eastern European.

Ok, I'll bite.
All you (2-3 members in this thread actually) Catholics who opt for the Eastern Rite the same way 99% of Trad-leaning Americans head for a Tridentine Latin Mass chapel (Roman Rite) --

There's just one problem.

You're a small minority. What are the chances there's a nice young lady at that ONE Eastern Rite chapel for your son, or a nice young man for your daughter to marry?

In the Trad world, at least we have the TLM to unite us. There are a lot of Trads nationwide, and even worldwide. We are all comfortable with the same Mass.

If you/your son/daughter DID meet a good spouse at a different Rite, which rite would you go to as a family and raise your children in?

This is alone a good reason to stick with Western ways and the Roman Rite.

Ok, I'll bite.
All you (2-3 members in this thread actually) Catholics who opt for the Eastern Rite the same way 99% of Trad-leaning Americans head for a Tridentine Latin Mass chapel (Roman Rite) --

There's just one problem.

You're a small minority. What are the chances there's a nice young lady at that ONE Eastern Rite chapel for your son, or a nice young man for your daughter to marry?

In the Trad world, at least we have the TLM to unite us. There are a lot of Trads nationwide, and even worldwide. We are all comfortable with the same Mass.

If you/your son/daughter DID meet a good spouse at a different Rite, which rite would you go to as a family and raise your children in?

This is alone a good reason to stick with Western ways and the Roman Rite.

It’s a valid point.  But, let’s face it, things aren’t going well in the traditional chapel scene either. There are so many divisions now that your son or daughter may only be limited to future spouses from whatever group or sub-group you affiliate with.  If you are a resistance family, a hard core SSPX loyalist family may not let your kids near their kids, the same could be said about families who are CMRI, FSSP, SSPV, etc.  

It’s getting tougher to help your kids find good and compatible spouses no matter where you plant your roots during this crisis.

I have been every now and then to Syrian Catholic and other Eastern Catholic rites. I have no intention of switching rite of course, but they are ok to assist at because many of them are mostly unchanged. I don't live in the west of the world, though I am a Roman Rite Traditional Catholic. I think the Eastern Catholic rites that have existed for a long time are all good and holy, just like our TLM. The Liturgy of St. James, both its text and the video (can find only Orthodox, but I think Catholic is same) http://www.newadvent.org/fathers/0717.htm is a reverent liturgy. I personally dislike for myself the idea of us Latin-rite Catholics turning away from our difficulties, rather than working to restore Tradition in the Latin Church, along with the Eastern Churches in communion with Rome. But if someone, weighing all the circuмstances, wants to choose that as the best for him and his family, I think that's legitimate.

Some texts from that Liturgy, from New Advent: "The Priest.

I O Sovereign Lord our God, contemn me not, defiled with a multitude of sins: for, behold, I have come to this Your divine and heavenly mystery, not as being worthy; but looking only to Your goodness, I direct my voice to You: God be merciful to me, a sinner; I have sinned against Heaven, and before You, and am unworthy to come into the presence of this Your holy and spiritual table, upon which Your only-begotten Son, and our Lord Jesus Christ, is mystically set forth as a sacrifice for me, a sinner, and stained with every spot. Wherefore I present to You this supplication and thanksgiving, that Your Spirit the Comforter may be sent down upon me, strengthening and fitting me for this service; and count me worthy to make known without condemnation the word, delivered from You by me to the people, in Christ Jesus our Lord, with whom You are blessed, together with Your all-holy, and good, and quickening, and consubstantial Spirit, now and ever, and to all eternity. Amen.

Prayer of the standing beside the altar.

II Glory to the Father, and to the Son, and to the Holy Spirit, the triune light of the Godhead, which is unity subsisting in trinity, divided, yet indivisible: for the Trinity is the one God Almighty, whose glory the heavens declare, and the earth His dominion, and the sea His might, and every sentient and intellectual creature at all times proclaims His majesty: for all glory becomes Him, and honour and might, greatness and magnificence, now and ever, and to all eternity. Amen.

Prayer of the incense at the beginning.

III Sovereign Lord Jesus Christ, O Word of God, who freely offered Yourself a blameless sacrifice upon the cross to God even the Father, the coal of double nature, that touched the lips of the prophet with the tongs, and took away his sins, touch also the hearts of us sinners, and purify us from every stain, and present us holy beside Your holy altar, that we may offer You a sacrifice of praise: and accept from us, Your unprofitable servants, this incense as an odour of a sweet smell, and make fragrant the evil odour of our soul and body, and purify us with the sanctifying power of Your all-holy Spirit: for You alone are holy, who sanctifies, and are communicated to the faithful; and glory becomes You, with Your eternal Father, and Your all-holy, and good, and quickening Spirit, now and ever, and to all eternity. Amen." ... (see the link for more; basically, it's an entirely orthodox Catholic traditional Liturgy).