The problem is any unit of information can be reinterpreted as "hate speech". If someone sends a cat photo to someone else and the receiver perceives it as hate speech then the community will get to determine if it really is hate speech and the sender gets punished based on the subjective interpretation of the community.
Obscenity is not clearly defined and neither is hate speech. You could send what you thought was an innocuous message and maybe at the time you sent it the community perceived it as innocuous, but what about in a few years when the interpretation of your message is different and community standards have changed?
You still get punished for having send something obscene even if during the time you sent it it was innocuous? The community determines what is and isn't obscene according to an always changing standard. Hate speech has lists of words and phrases in some database, combined with how some people feel at some time about what you said? So feelings ultimately govern whether or not you get punished?
This could have an unintended chilling effect. How do any of us know whether or not something we post today will not be hate speech tomorrow? What about young people who will have no way to even understand what is and isn't considered obscene or offensive? Most people have said a lot of hateful stuff when young without even understanding it was hateful.