When you aspire to something, you strive for it, it is something you are aiming at. From my understanding, the meaning of this sentence is that aspiring to kindness might be seen as normal. I hope that answers your question

Here, it probably means something to which one would aspire, that is, something one would hope to achieve. In other words, the writer is saying that it is normal to hope for random acts of kindness. Does that make sense in your context?