The Seafarer and The Wanderer, two of the most well-known and studied Old English poems, were most likely composed around 750 CE, roughly contemporaneous with Beowulf. Like Beowulf, these two poems, as your question suggests, contain references to the speaker's pagan and Christian belief systems, sometimes within the same lines. It becomes clear as we explore these poems, which discuss the effects of exile on the speakers, that their belief systems overlap each other so that each speaker often unconsciously expresses a pagan belief and, at the same time, recalls that he has a new religion—then employs conventional Christian imagery.
In The Seafarer, for example, the seafarer makes no Christian references in the first 75 lines as he describes the hardships he has endured as an exile at sea—"I, wretched and sorrowful, on the ice-cold sea dwelt for a winter" (1.14)—an exile that he seems both to love and hate by turns. In a particularly clear pagan reference, the seafarer explores the world's impermanence:
Always and invariably, one of three things
will turn to uncertainty before his fated hour.
Disease, or old age, or the sword's hatred
will tear out the life from those doomed to die. (2.68–71)
Harking back to his pagan belief in fate and doom, the seafarer points out that men live only until their "fated hour" and that disease, age, or warfare will kill them when doom strikes. Fate ("wyrd" in Old English) is an actor in this drama of life, not the Christian God.
In a lament that some scholars believe places the poem in the genre of elegy, the seafarer bemoans the loss of his world in what is often called the ubi sunt (Latin for "where are") trope:
The days are gone of all the glory
of the kingdoms of the earth, there are not now kings....
All that old guard is gone and the revels are over—
The weaker ones now dwell and hold this world...
The glory is fled, the nobility of the world
ages and grows sere.... (2. 80-89)
The seafarer looks backwards to his pre-Christian world in which powerful warrior-kings and loyal warriors celebrate victories in their mead-halls, only to be replaced by "weaker ones [who] "hold this world." Given this clear preference for his pagan world, the seafarer may, in the moment of emotional recollection, be saying that Christians are the weak people who now control the seafarer's world.
The last twenty lines or so contain a dramatic turn from the seafarer's lament for his lost world, and he shifts to a conventional, perhaps politically correct, exploration of the benefits of Christianity:
A fool is the one who does not fear his Lord
...Blessed is he who lives humbly—to him comes forgiveness from heaven. (2.106–197)
The seafarer's focus shifts so abruptly in the last section of the poem that one cannot help but think this re-focus on his Christian belief system is an afterthought—he is suddenly aware that he is dangerously close to blasphemy and pulls himself back to his new but as-yet not internalized belief system.
The Wanderer, like The Seafarer, is about exile, but the speaker acknowledges his Christian belief system in the poem's opening lines:
Often the solitary one finds grace for himself
the mercy of the Lord, Although he, sorry-hearted...[moved] along the waterways, the ice-cold sea,
tread the paths of exile. Events always go as they must. (2.1–5)
Here, in the space of five lines, the wanderer manages to acknowledge his Christian belief system, on one hand and to use a very common reference to fate (or "wyrd"), on the other hand—a reference that we see in "The Seafarer" and Beowulf often in proximity.
Like the seafarer, the wanderer is an exile and laments the loss of his pre-Christian world in terms very similar to the seafarer's:
He [that is, the wanderer] remembers hall-warriors and the giving of treasure
How in youth his lord (gold-friend/goldwine) accustomed him to the feasting.
All the joy has died! (2.34–36)
The old life of feasting, comradeship, and joy has passed away, and this new life with a belief system that is as strange to the wanderer as it is to the seafarer creates in the wanderer an intense longing for what he can no longer have:
The halls decay, their lords lie deprived of joy,
the whole troop has fallen, the proud ones, by the wall. War took off some. (2.78–80)
What the wanderer is observing and then feeling is not only the loss of companionship and feasting with his lord, the ring-giver, but also the disappearance of even the physical remnants of his former life—the mead-halls, symbols of power and communal life, are falling into the landscape, leaving no trace of a vibrant culture.
Like the seafarer, however, the wanderer accepts the loss of his pre-Christian world and ends the poem with another very conventional Christian belief:
It is better for the one that seeks mercy
consolation from the father in the heavens
where, for us, all permanence rests. (2.114–115)
Considering that the poem consists of 115 lines, and about ten actually reference some aspect of Christianity—including the rather perfunctory last two lines, given with no enthusiasm—we cannot but conclude that both poems, but especially The Wanderer, are truly laments for a world that has passed away and has been replaced by one that sparks no life into the speakers.