I have tried to answer this question by showing some Christian teaching on the "extreme sports" of previous centuries, which are pretty extreme by modern standards too.
Jousting was very dangerous and many people were killed and injured; other tournament sports such as the melee also had a high casualty rate. In the twelfth through fourteenth centuries, the Catholic Church tried to discourage jousting, partly because of the possibility of these sportsmen killing themselves or others. The following is typical - Canon 14 of the Second Lateran Council (1139):
We entirely forbid, moreover, those abominable jousts and tournaments in which knights come together by agreement and rashly engage in showing off their physical prowess and daring, and which often result in human deaths and danger to souls. If any of them dies on these occasions, although penance and viaticum are not to be denied him when he requests them, he is to be deprived of a church burial.
Similar prohibitions were stated in the Council of Clermont (1130), of Rheims (1131), Lateran III (1179), and Lateran IV (1215), and in Papal decrees (eg of Clement V, Pope from 1305 to 1314). They were annulled by Pope John XXII (reigned 1316-1334) because the penalties were felt to be too harsh, and were catching too many people. Some effort had also been made, in terms of technique, better armour, etc., to make the sport safer for the participants. (Jousting in medieval and renaissance Iberia, Noel Fallows, Boydell Press 2010, p173-4.)
This is certainly in line with Catholic / general Christian thinking on the value of human life, including one's own life; deprivation of church burial was also characteristic for suicides. However, these decrees do not impose a penalty of, say, excommunication; and it was accepted that jousting was legal under the civil law. So this attitude towards jousting doesn't seem to me to be so "strong" - it's just that the particular way the sport was practiced at the time was felt to be excessively dangerous, and a later pope ultimately rescinded the decrees. Modern sports, even the ones you mention, are far, far less risky. There is also a strong ethos for safety and responsibility among the participants in extreme sports, including use of proper equipment, having plenty of training, and so on. This reduces the danger and the moral objection.
Other considerations might include the frivolous nature of these events. Football, for example, was banned by the Puritans in England for this reason, in addition to the violent way the game was played, and its connection with betting. The objection on the grounds of danger is basically similar to the jousting case. Philip Stubbes wrote (Anatomy of Abuses, 1581):
As concerning football playing, I protest unto you it may rather be called a freendly kinde of fight, then a play or recreation; a bloody and murthering practise, then a felowly sport or pastime. [...] hereof groweth enuie, malice, rancour, cholor, hatred, displeasure, enmitie, and what not els; and sometimes fighting, brawling, contention, quarrel picking, murther, homicide, and great effusion of blood, as experience daily teacheth. Is this murthering play, now, an exercise for the Sabaoth day? is this a christian dealing, for one brother to mayme and hurt another, and that vpon prepensed malice, or set purpose? is this to do to another as we would wish another to do to vs?
Again, modern sports are a bit better at avoiding brawling and homicide. It's true that the objections other than danger still apply - on that basis, someone could argue against tiddlywinks - but if participants are being responsible about threats to life and limb, it's harder to say that a sport should be considered immoral in itself.
