Um...lilinawin ko lang para, well, para malinaw sa lahat

Hindi ako expert sa theology so I can't really make a competent judgment on the lyrics of the song

hehehe. But be that as it may, some thoughts I'd like to share:
* The end-all and be-all of Catholic theology---at least, for laymen who want to know more about their Catholic faith---is the Catechism. I'll say more about the Catechism (including some points that everyone should know), but at this point (or at this paragraph

hehehe) I'd like to say that, basically, if a song's lyrics seem to contradict anything that you know is in the Catechism, then at the very least you try to consult a priest and have that priest check the lyrics' doctrinal content (kung hindi man tanungin ang competent authority ng inyong parish or diocese).
I'll give you really dumb and extreme examples to drive the point home: kung may kantang sinasabi na the Virgin Mary is on the same level as (or---ack!---even higher than) the Holy Trinity; Jesus Christ didn't establish the Church (re: Peter the rock episode in the bible) and the allusion to Peter was just a figure of speech; John the Baptist, not Jesus Christ, is the Messiah. Of course, every Catholic knows (or should know) that these are inconsistent with the magisterium of the Church, so any song with lyrics of those nature are obviously disallowed, to the point that if you do know that a song has questionable doctrinal content, then you don't even need to ask if there are any regulations (old or new) as to whether you can even sing them in the liturgy
Now, back to the Catechism. The Catechism is, on record, the document that has the definitive version of what the Church teaches to Catholics. If you really have the time (with emphasis on
time), it's worth reading the Catechism from cover to cover; as in, kung tamad-tamad kayong maghagilap ng mga bagay-bagay tungkol sa doktrina, then you should read the Catechism next to the Bible. Kung nahahabaan naman kayo sa Catechism---meron lang naman siyang 800-900 pages sa book version nito, depende sa nagprint nito

---then you can just buy yourself the Compendium of the Catechism, which is at a more reasonable 200-something pages lang.
BUT (and this is what I was meaning to say)...don't think that the Catechism is "the" final word on Catholic doctrine. The Catechism is merely a
summary of the whole of Catholic teaching but, as Fr. JBoy Gonzales himself told me (in a personal conversation), Catholic teaching is worth more than the number of pages of the Catechism. Marami pang ibang sources na pinanggagalingan ng Catholic teaching, and it's not enough that you rely on the Catechism alone (that is, kung talagang gusto n'yong pangatawanan na pag-aralan ang Catholic theology and teaching). Kumbaga, the Catechism is just a guidepost (but a really large guidepost at that), and if you really want to learn more, then there are much, much more places to learn about Catholic teaching. At the very least, the Catechism gives you a head start.
So how do we go about with using the Catechism for checking if your lyrics are consistent with Catholic teaching? If it were me: read the Catechism. Read the lyrics. Does any part, even one sentence of the lyrics, seem to be inconsistent with Catholic thought? Do more research. Still not satisfied with what you've seen so far? Go ask a priest (plus points if that priest belongs to the faculty of a seminary or school of theology

). Still not satisfied? Then bring the matter to your parish or diocese and let them decide about it (at least, by then, you already did your homework na

)
* Tama si Alex regarding charismatic songs. The gatherings or activities of charismatic groups are
per se not covered by liturgical norms because, yes, those activities are
not part of the liturgy. A quick check is this: kung ang isang religious activity ay hindi kasama sa mga liturgical books ng simbahan (e.g. wala sa missal, sacramentary, marriage rite, funeral rite etc.), then it's not a liturgical activity. So, really, wa epek 'yung mga liturgical guidelines sa mga ganung sitwasyon. Hence, no need to ask if a song is liturgical or not if, for example, you're going to use it in your org's prayer service or in your parish's "Living Rosary" (because the rosary is, per se, not a liturgical activity; it is a devotional prayer).
Now, as to whether those songs are consistent with Catholic theology....
* Sinabi ko na ito somewhere, but it's worth mentioning. Maraming confusion as to what the GIRM and MS are for. Basically...
...if you're asking about the quality or the suitability of a song (content and music) for the liturgy, including mass, then you should read Musicam Sacram. Take note that MS contains guidelines not just for the mass, but for the Divine Office (Liturgy of the Hours) as well. So don't make the mistake of assuming (like many others do) that the Musicam Sacram is a set of guidelines "for mass songs". It's not just "for mass songs" but "for mass songs and songs for use in other liturgies".
...if you're asking about how you're supposed to sing a particular song in the mass (e.g. can repetitions of the Kyrie be made? do you sing Alleluia on Lent and Advent?), then you should read the General Instruction on the Roman Missal.
Of course, both guidelines contain other items not related to songs (e.g. MS has general guidelines for choirs and singers; GIRM has guildelines for, say, how altar servers are to conduct themselves in the altar), but the distinctions I emphasized above are regarding how you should use each document when you need to consult them regarding songs
Unfortunately...it seems that there is very little, if any, content that refers to song lyrics. Kahit sa Redemptionis Sacramentum or sa Sacrosanctum Concilium, parang hindi ito masyadong nabigyang-diin. My guess is that the logic behind this is because those documents were aimed at certain aspects of the liturgy, and in particular, more on the conduct of rites and ceremonies. But if it's a question of Catholic theology or Catholic teaching, then those documents (probably) are not the best place to look for answers and you probably need to look elsewhere like any regulations or Church laws regarding Catholic doctrine na. I could probably even argue that
it's probably also a matter of Canon Law (see Canon 1369), but this is most likely an extreme case na (and, of course, I'm not a Canon Lawyer either, so I could be wrong in that respect

)
(See? That's why I said earlier, hindi sa Catechism ang final word sa Catholic teaching. Obviously, there is a huuuuuge amount of material that we all need to read

) )
* I do agree with the stand taken by the blogger in the link Alex posted. Wala namang song na bininyagang Katoliko o Protestante o Born-again o maski Muslim o Hudyo in the first place..we only have Catholic/Protestant/Born-again/Muslim/Jewish songwriters, not songs

So I think medyo unfair na sabihing komo hindi Katoliko ang gumawa ng kanta, bawal nang kantahin sa misa. In that respect, you are judging the songwriter, not the song. Ni hindi mo pa nga nababasa 'yung lyrics ng kanta, sinasabi mo na kaagad na hindi siya bagay sa Catholic liturgy? If the song doesn't seem to contradict Catholic teaching naman, then perhaps it's safe that lyrics-wise the song
may be allowed in the liturgy (better if your local liturgical authorities have given their approval).
Now, as to whether the
music is appropriate for Catholic liturgy...
* And finally...about the song itself. Sorry, but I'm not a big fan of Don Moen and of Hillsong

Regardless of whether any of their songs are not in contradiction with Catholic teaching, hindi ko tinatangkilik (at lalong hindi ko tinutugtog o pinapakanta) ang mga ganung kanta sa misa. Sa opinyon ko rin, hindi siya bagay kantahin sa misa maski na i-rearrange mo pa siya nang hindi pop ang datin.
So perhaps I'm the wrong person to ask because my answer will be...no, no, and a big, big NO...because I avoid Don Moen and Hillsong like the plague