To explain better: It's more about your intentions and thoughts than your acts. It's not about what you do, but what you think. Not intending to harm animals and keeping this for the time being, it means you are fine. No matter what you have done in the past.
People who have done these bad things repeatedly will probably will keep having these bad thoughts and will be harder to overcome them because habits are habits. These people may say that they will not do it again, but since it's become a habit they will probably do it again, unless they somehow snap out of it. It's similar to drug addicts. These people are probably getting thrills or a high by harming people or animals, so they need to replace these with some wholesome activities that excite them like swimming or sports.
But if you have done something bad once, then there's no need to worry, because you don't have that habitual thought pattern.
So you can see in my replies I'm placing all the emphasis on how to stop doing bad things, because that's the most important thing. It's practical. If the Gods were like the Jewish god and said "well, we will continue being angry at them and these people will never be accepted by us" to people who have done bad things but are self-aware, do you think that will stop their bad behavior? Or they will just say "well, since the Gods don't accept us, I might well keep doing the bad things I'm doing, since there's nothing I can do about that"?
Of course not. That's why the Gods are pragmatic and expect us to fix anything bad we have done ourselves. They don't want groveling and feeling sorry, because that doesn't work and keeps the bad past going instead of fixing it and replacing with a good present.