The list of offenses that the law talks about includes a whole list of things that aren't remotely hate speech: they include things such as the creation of a criminal or terrorist organization or illegal distribution of pornography (pornography is not per se illegal, but you cannot, for example, sell it to minors).
The goal of the law is basically to enforce offenses that are commonly committed online by deputizing social media companies. And this is where the actual problem lies; the law does not regulate anything that isn't already an offense, after all.
1. Many of these social media companies do not even have a legal presence in Germany and it is questionable whether Germany even has jurisdiction under current EU law.
2. Even if Germany has jurisdiction, having social media companies adjudicate the legality of online content (even where there is a legitimate interest and we are not dealing with offenses that affect freedom of speech) is a bad idea in too many ways to count. The social media company is incentivized to err on the side of banning content; they generally do not have the resources and/or personnel with adequate legal training to properly adjudicate the issue in many cases; and if they get things wrong, there is often no practical way to appeal their misjudgment.
3. The law may (due to its crude mechanisms) have a chilling effect far beyond what any that current laws create, even though on paper we're talking about the same offenses. That's because the legal system generally subjects potential prosecution for many of these offenses to a high level of scrutiny in order to protect freedom of expression. It is unlikely that Facebook and Twitter are going to do the same.
4. As a result, the law is probably headed for a collision course with the Federal Constitutional Court at the earliest opportunity.