Out the gate, it must be stated that being unclean does not equate to being a sinner. Things such as taking care of your deceased family members, a menstrual cycle, birth, and removing an animal carcass from a drinking source are not something that God considers sin. They are, however, things that separate us from him temporarily. In that sense, it can feel or come across a bit like a sun but there is definitely a distinction.
Uncleanness, in most cases has to do with death, which is the penalty for sin. As such, while God recognizes the reality of these things, it is not something he celebrates or wants around him. These reminders cause us to be temporarily “unclean” meaning God essentially wants some space. We are to wash in moving water (literally, just take a shower) and then we’re clean at sundown. Until both criteria are met, God asks that we do not approach his throne. The way I think of this is as a married couple. If one spouse does something rather innocent but it triggers the other into a past trauma, they may be a bit distant for a short while. While neither party is truly to blame here, there is a small wedge of separation. Communication (prayer) would not necessarily be damaged but intimacy (approaching the throne of God via the temple) will be.
For “ervah matters,” (Lev 15 and 18, among others) meaning sexual uncleanness, most fall into some category of incest but there are other categories. Perhaps the most debated in modern times is that of menstruation and child birth. It feels unfair to many that God “punished women” for things that he designed for their bodies to do. While this is certainly understandable, and a position I’m largely sympathetic toward, from God’s perspective, every cycle is the loss of a potential life. Similarly, a man’s night emissions leave the man in the very same state of uncleanness. Child birth, and the pain of it, is again a reminder of the punishment of sin. Beyond this, both cause the woman to lose blood in some way. The Bible states that life is in the blood (Lev 17) and loss of blood is generally associated with death; that association makes you unclean - that is, separated from God’s presence for a short time - regardless of gender.
In the case of unclean animals (Lev 11), nearly all of the animals mentioned as unclean sustain their life by eating other animals. That is, they live by creating death. The other major category are what I term “garbage truck” animals - namely pigs, shellfish, and insects. While a trash truck serves an immensely important role in society, it is not something you would expect to walk away from feeling clean. Similarly, these animals are not something that God considers appropriate for consumption.
In Mark 7, we see that Jesus declared allt things clean, clarifying that cleanliness has to do with the state of the heart, rather than anything we ingest. In the context, this was speaking specifically of washing hands in a ceremonial manner. The primary teaching here was to honor the scriptures above tradition, not forsaking what is truly important in favor of some minor spiritual flex. How true is this today? We so often wish to look holy and, in so doing, look over the very people we should care for the most. Jesus would call this state of the heart far more unclean than someone who ate a strip of bacon. While pig is still not considered suitable for eating, just as touching a dead body still requires a shower, the uncleanness that follows, is much preferred to a callous heart.
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