This first meme uses authority fairly explicitly to convey it's message. In this meme, it derives it's authority from the religious text of Christianity, the Bible. It doesn't use a specific quote, or even claim to use a statement from the Bible, but rather attacks Christians who support trump for supporting a man who "can't name any[thing]" from their religious text. The meme also goes on to use one of the central structures of Christianity, the act of asking God for forgiveness, as an assertion of authority. By saying that Trump does the opposite of these specific practices and being in opposition to these authority sources, it implies that Trump is not a Christian, and therefore challenges Christians who support him. This meme is using the Logic of Continuity in order to establish and assert its claim: it is using the established authority derived from a simple understanding of the religious text and the regular practice of repentance to convey it's message. Overall, it invokes the authority of these structures in a digital space in order to show that Trump is not a Christian for not following these specific authority structures and challenges Christians who support trump when he, according to this meme, is not very Christian.
Unlike the first Trump meme, this second meme is more like most other memes I've seen so far in that it does not explicitly invoke an authority structure to convey it's message. It can be argued, however, that it implies an understanding of general Christian authority that the reader must draw on in order to understand the meme's authority source. This meme draws on the idea that to Christians, there is no such thing as a "good Christian". This comes from the authority of the theological idea that Christians are all sinners just like everyone else, and that the cliche "nobody is perfect" is true. The one that that makes this meme similar to the first is that this, too, is using the Logic of Continuity in order to extend this idea that everybody is equal based on the theological and textual authority that it is assuming its audience has an understanding of (since it implies the authority that it draws from rather than explicitly referencing it). In doing so, it challenges the belief that Trump is a model Christian who the Christian voters should vote for purely because he's a "good Christian" doesn't make sense according to Christians' own beliefs
Together, these memes have used the idea of authority, either explicitly or implicitly, to use the online as a continuation of the authority structures that have been established offline in order to maintain and establish the idea that Trump is not a Christians and it is hypocritical for Christians to support Trump for the reason of him being a Christian because his claims to Christianity don't fit with the Christian beliefs or authority structures.