Agendas are different than Aspirations
In most CoD games, there's both an "innate axis" - a fundamental, distinction about characters they are unable to change - and a "social axis" - a general outlook that binds them, but can be changed over time (even if there's social repercussions.)
For Demons, they know that there is a powerful entity out there that would be pleased with their destruction. Left unchecked, it's not a question of if the GM catches them someday - just when. Think more in terms of Changeling Courts than Vampire Clans, if it helps.
I don't know the passage offhand, but it is stated that most fallen Angels don't live long enough to become Demons - in other words, if an Angel was so captivated by art that it Fell and just obsessively went to a museum, or befriended an artist and took protecting them as a personal goal, it would not take long before it ran across its "former coworkers". If it's not proactive about its survival, this Demon would be toast.
That being said, while survival is important to Demons, the most interesting characters strive for something beyond mere survival. For example, if I were to ask you personally about your hobbies, I doubt "staying away from lion dens" would be one of your highlights, even though that's kept you alive your entire life so far. On the other hand, if vegetarianism is important to you, that might be worth a mention, even though most people "eat food."
So, some Demons (like particularly zealous Saboteurs) might have major Aspirations that are in line with that Agenda, others (like Integrators) might not.
With all that in mind, let's look at some examples:
Ink is obsessed with art; it's more than just shapes and colors, right? Ink aligns himself with the Inquisitors - perhaps learning the secrets of the soul will help him foster humans' creation of art - but he wants to be left alone by the GM to focus on what's important to him. [Conversely, he's a well-respected Tempter, fostering mankind's art is like shepherding their souls. The one thing he doesn't doubt about Hell is that it'll be beautiful.]
It calls itself Green. Its parameters were simple: "Protect the environment." How does one Fall from that? Even when it fails to stop a massive oil spill, its parameters still read "Protect the environment." In fact, it's never heard anything from the GM since; it's an Exile (even if it doesn't know it.) It is unswayed by the pleas of the Demons, since the Angels act like it doesn't exist, even when it destroys them for trying to harm endangered animals. However, every one it kills propels it closer to being a Sliver... [Note: Exiles are covered more in-depth in DtD Storyteller's Guide]
She is The Judge; she was once a defender, whose charge was slain by a two-faced thing that could walk through walls. Refusing to accept her failure, she became an Antinomian Destroyer, and has resolved to rid the world of these "blights of Creation." Even her fellow Integrators are taken back at the scope of her undertaking; she's said she'll happily turn herself in when all her targets are destroyed, but how could she ever hope to do so? [Conversely, she could be a passionate Saboteur, taking all the preternatural things, but saving the GM for the last...]
He fell when he developed a conscience; Mr. Knight saw the injustice of the world and felt hurt by it. He has a Dual-Agenda (DtD, page 121) of Integrator-Saboteur, but this based from a steadfast determination, rather than confusion. Instead, he's both revered (and notorious) for sidings "with" or against the GM, depending on how "just" its plans were. If it only knew how many Angels it was causing to Fall by sparing their lives... [Conversely, he could be Uncalled (DtD, page 78) by choice. His is a solitary life, but the hardships demand he grow stronger for the experience]
My answer primarily deals with "How might a lone Demon pursue this passion?"; it's worth mentioning that if you are looking for a way that the above goals might bind multiple Demons together, they can be well represented with Agencies - detailed in DtD Player's Guide.