Catholic Identity

Are there certain ideas that are accentuated in these memes that speak to the perceived beliefs of this community?
The memes used and created within the Catholic religion are fairly surface level. Most of them are easy to understand to insiders and outsiders. With that, there seems to be a discrepancy within this culture because while many memes are easy to understand and laugh with, the rest are complex, intricate, and very confusing to any outsider. There is no middle ground of understanding. There is a distinct line to keep those outside the religion out and those who are dedicated, in.
For example, this first meme is easy to understand and funny even to those outside the religion. It is a religious take on a meme with Kanye West (below).

Source

As for this meme, it does not make sense unless you are familiar with the Bible story about Sodom and Gomorrah. Even some Catholic, Jewish, or Protestant believers won't get it because it is a more obscure reference. 

Additionally, 

Why do you think these are highlighted in these memes? What messages are being communicated by the ways these are presented?

Catholicism is a religion that has many practices, rituals, and traditions. In some memes, you can see how this comes through. This is a religion that takes itself very seriously and expects others to do the same. While the people creating memes are more likely to view it more lightly and maybe less seriously, I feel that they do not necessarily represent the religion well. That is why there is this huge discrepancy between who can and cannot understand the more "religious" memes representing the Catholic faith. The difficult to understand memes are for those who know the religion and take it seriously, because these memes are typiclly not as well executed and are not as funny. 

Finally,

How do your observations relate to claims about how religious identity is presented and negotiated in digital culture as express in the class lecture and readings this week?

There is no such thing as a "half-ass" Catholic. When someone truly identifies with being Catholic, it is their whole life and worldview. If you really believe, there is no room for wavering and doubt. Bellar says it best when he states, "Lived religion is an approach that sees religion as dynamic, experiential and rooted in the daily life of its practitioners" (Bellar et al, pg. 7). Memes can be a form of expressing this lived religion. Because Catholicism and lived religion go together quite perfectly.