These are often in direct conflict. One will take precedence over the other, and without iron-clad laws, it will be the one that favors those in power instead of the people.
If your government passes a law promoting a special status to a group of people as except from criticism in order to promote "tolerance," then it could be argued -in court- that speaking out against such a law encourages violence and hate against that group of people by making it more likely that violence and hate will be directed toward them because they no longer have that special status as being exempt from criticism. Since criticism can encourage hate, the government was therefore right to pass a law outlawing free-speech with regards to that group.
After that, just pass some porkbarrel legislation in with that hate speech law that increases government power to continue to suppress the people. Publicly, they are passed as a way to discourage hate against a particular group. Sure let the police do everything in their power to prevent the "bad people", the "rabble rousers', the "extremists". Anti-encryption laws, surveillance, we need that to "protect you" from "them." But actually, they are used by governments to put people on watch lists so they can be targeted for criticizing the government by nailing them for unrelated crimes... all in the name of "tolerance" and "anti-hate" and "anti-terrorism". See where this is going?
Encouraging violence (non-immediate), hate and other forms of intolerance towards a specific person or group of persons must be a protected right in order for freedom of speech to mean anything. The point of free speech is to protect other freedoms, like privacy, the right not to be surveiled, right to publish, organize with one's peers, and without it, those other freedoms wither.
"Should I go to a rally or hear a speaker sponsored by this political action group this evening? I better not because I might get put on some government list, passed via anti-intolerance laws, and they could throw me in jail for any little thing if they found out I attended." -The death of freedom of assembly.
This confuses the symbol with the object. Very simple error, but of great consequence.
The symbol, the expression of intolerance is fine; what we don't want are intolerant people.
The speech of those intolerant people lets us know they are intolerant so we can address their concerns publicly. That means intolerance must be protected so they can continue to let us know of their views and we can continue to counter it via logic, reasoned arguments and evidence. Using the government to forcefully suppressing their expressions of hatred, 1) does not change the fact that they really are intolerant, merely hides it from view, and 2) does not change the actual amount of intolerance in society for the better because it precludes the possibility of addressing it in a public way, and therefore does not limit it spreading further.
Intolerance simply breeds just as much as tolerance in societies, relative to the actual % of the population with those views. They are literally counter-productive. They actively do exactly what they were supposed to prevent. This isn't even going into the insanity of those promoting hate using such laws in court against those who point out that such speech is hateful. Merely pointing the truth is "hateful" and thus not protected speech. Welcome to the Netherlands.
The people of Germany, or at least the government, has already forgotten what protects against such crimes being committed in the future, as exemplified by their laws. They are even willfully importing the most intolerant people on earth into their society en-mass with no plans for how to bring them up to speed with western notions of freedom out of a sense of guilt. Without really understanding the specifics, sometimes trying very hard to prevent something ends up producing that something.
Not free speech issues here.