Catholic.com says that:
Although Latin-rite Catholics are usually baptized by infusion (pouring), they know that immersion (dunking) and sprinkling are also valid ways to baptize. Fundamentalists, however, regard only baptism by immersion as true baptism, concluding that most Catholics are not validly baptized at all.
Although the New Testament contains no explicit instructions on how physically to administer the water of baptism, Fundamentalists argue that the Greek word baptizo found in the New Testament means “to immerse.” They also maintain that only immersion reflects the symbolic significance of being “buried” and “raised” with Christ (see Romans 6:3-4).
It is true that baptizo often means immersion. For example, the Greek version of the Old Testament tells us that Naaman, at Elisha’s direction, “went down and dipped himself [the Greek word here is baptizo] seven times in the Jordan” (2 Kgs. 5:14, Septuagint, emphasis added).
But immersion is not the only meaning of baptizo. Sometimes it just means washing up. Thus Luke 11:38 reports that, when Jesus ate at a Pharisee’s house, “[t]he Pharisee was astonished to see that he did not first wash [baptizo] before dinner.” They did not practice immersion before dinner, but, according to Mark, the Pharisees “do not eat unless they wash [nipto] their hands, observing the tradition of the elders; and when they come from the market place, they do not eat unless they wash themselves [baptizo]” (Mark 7:3–4a, emphasis added). So baptizo can mean cleansing or ritual washing as well as immersion.
A similar range of meanings can be seen when baptizo is used metaphorically. Sometimes a figurative “baptism” is a sort of “immersion”; but not always. For example, speaking of his future suffering and death, Jesus said, “I have a baptism [baptisma] to be baptized [baptizo] with; and how I am constrained until it is accomplished!” (Luke 12:50) This might suggest that Christ would be “immersed” in suffering. On the other hand, consider the case of being “baptized with the Holy Spirit.”
In Acts 1:4–5 Jesus charged his disciples “not to depart from Jerusalem, but to wait for the promise of the Father, which, he said, ‘you heard from me, for John baptized with water, but before many days you shall be baptized with the Holy Spirit.’” Did this mean they would be “immersed” in the Spirit? No: three times Acts 2 states that the Holy Spirit was poured out on them when Pentecost came (2:17, 18, 33, emphasis added). Later Peter referred to the Spirit falling upon them, and also on others after Pentecost, explicitly identifying these events with the promise of being “baptized with the Holy Spirit” (Acts 11:15–17). These passages demonstrate that the meaning of baptizo is broad enough to include “pouring.”
It further goes on to say that much of the earliest Christian art shows either pouring or sprinkling, or if standing upright in a river, having water poured from a cup or jug over the head. An early baptismal font found in Nazareth is obviously far too small for immersion.
I’m not aware of anything we Romish do that is not in the Name of Father, and of the Son, and of the Holy Spirit. I thought that we are fully in agreement on that.
I can speak only for the position of the Orthodox Church, whether we "qualify' as "fundamentalists" or not.
The Greek meaning of baptiso is to immerse repeatedly. This is not to be confused with bapto which is related but different. This is why the Orthodox Church considers one-time immersion invalid baptism.
Immersion logically implies that something is completely covered or surrounded by that into which one is being immersed. This invalidates sprinkling.
Thus, pouring is acceptable where living water or baptismal pools are unavailable, because pouring envelops the person being baptized completely; sprinkling doesn't.
The concept of being "buried" is also met by pouring but not by sprinkling. If a Latin-Rite Catholic desires to cross over to Eastern Orthodoxy the bishop will do everything to determine if the person was baptized by triple immersion or triple pouring. If it is determined that the Catholic Baptism was done by sprinkling or if there is insufficient evidence to show that the person was baptized by pouring or immersion, the bishop will order baptism.
This is done for the benefit of the soul of the person and not as an affront on the sister Church. If a mistake is made by re-baptizing, the intention was honest and pure and we trust God will discount the second sacrament without penality. But, this way we can be sure that the person is received into the Body of Christ properly and within the Holy Tradition.
There are some far-off fundamentalists in every rite, including those Orthodox who insist that nothing short of triple immersion is true Baptism. Those are few and far inbetween and they do not represent the Orthodox Church in any way.
As regards your biblical verses (Luke 11:38, and related verses Mat 15:2, Mar 7:3), the word nipto means to wash. Luke uses the word baptiso because washing of the hands before meals was accomplished by dunking them into a bowl of water repeatedly. So, Luke did not refer to ceremonial bath, because that would be a practical impossibility in most cases, whereas washing your hands (by dipping) is hygienically prudent given that people handled live stock or had bowel movements and did other things that made their hands less then suitable to touch food (which was served in a common dish from which everyone dipped, and not on individual plates).