Does having freedom of speech mean that street preachers are protected while preaching the gospel?
Freedom of Speech
What is freedom of speech? Is it the freedom to say anything? No, because if you say certain things in public you can be arrested and especially if you make threats about dignitaries or public officials, including law enforcement agencies. You can also be convicted of “hate speech” if you spout racial slurs or derogatory language about a certain ethnic group or a people of certain color. One man was arrested in England for holding up a sign that said “Homosexuality is immoral .” The man had freedom to hold up signs, having the right and freedom to express his opinion, but when his opinion crossed over into insulting a certain group of people, the law stepped in. It is seen as “hate speech” and that person could be convicted of a hate crime. The framers of the U.S. Constitution didn’t have these things in mind when the ensured the American people they would have the right to free speech. They meant “the right to articulate one’s opinions and ideas without fear of government retaliation or censorship, or societal sanction, but as we know from experience, freedom of speech rights are not absolute.” 
Not Your Rights
A person’s rights to free speech when preaching the gospel are as varied as the land itself. Most civil and state authorities prohibit the distribution of Bible tracts in school, so you may have the right to free speech, but that doesn’t allow you to go down the school hallways preaching the gospel. Section 5 of the Public Order Act 1986 makes it a criminal oﬀence in Great Britain to use “threatening, abusive or insulting words or behavior with intent to cause harassment, alarm or distress.”  The European Convention on Human Rights guarantees the freedom of expression, including freedom of speech (Article 10) but also have similar restrictions to that speech. Many of the local authorities have similar language in their local law books, so even though you have a right to preach the gospel, in most places, no one has the right to publicly condemn or label someone or some group of people with hateful slangs and insults. I don’t think any Christian should ever do such a thing in private or public. It is contrary to Jesus’ command to pray for our enemies and do good to those who do evil to us, and love those who hate us (Matt 5:44). Having rights doesn’t always mean doing right.
What are your legal rights if you ever decide to share the gospel, either one on one with the public, or in street preaching to a larger crowd on a street corner? Most public street corners are where many street preachers go. He or she wants to go where the fish are. They might even bring a megaphone to reach a larger audience. When it turns bad is when you start naming certain people and associating them with certain sins. That may be true, but it can get you into trouble. Not only by angering others, but by coming across as a self-righteous hypocrite (to them). One man was threatened with arrest for publicly reading the Bible verse that says, “the cowardly, the faithless, the detestable, as for murderers, the sexually immoral, sorcerers, idolaters, and all liars, their portion will be in the lake that burns with fire and sulfur, which is the second death” (Rev 21:8). If the man had publicly read, “For the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord” (Rom 6:23), I think people would have still heard the gospel, without condemning them before they heard it. By the way, the Holy Spirit does the convicting. In most places, street preachers are protected by the first amendment rights to free speech, but even so, they are sometimes faced by law enforcement  who may not even know the preachers legal right to publicly preach. That doesn’t mean we turn belligerent. The police are doing their duty. We are to give honor to whom honor is due and obey those who are in authority (Rom 13:1-5). Only when man’s law contradicts God’s law do we ever obey God’s over mans (Acts 5:29).
You must realize that when you are bringing the gospel into the world, you’re entering enemy territory, so don’t expect a friendly reception. I have had dogs chase me, one cat brave enough to try, people slam doors in my face, people laugh me to scorn, a few swear at me, and yet, a few still hear what the gospel is all about. Even fewer will sometimes freely receive what Jesus freely gives. They have been brought to a repentant heart, they have confessed their sins, they have come to the cross for saving through Jesus, and they have trusted in the name that is most trustworthy of all! Even if you have the right to free speech and may share Jesus in public, others have the freedom of speech to heckle you or condemn or judge you. I know that is one of the most difficult things that the street preacher will face, yet they know they “will be hated by all for my name’s sake” (Mark 13:13a), and “If they persecuted me, they will also persecute you” (John 15:20). The street preacher, or any believer, that has been or is being persecuted, knows that a blessing comes with it (Matt 5:11-12).
Certainly, many businesses and government and state offices restrict the freedom to publicly preach the gospel and even pass out Bible tracts. The same is true in some public and private transportation avenues like jet aircraft, trains, subways, and buses. All we can do is all we are able to do…legally while showing respect and honor to all men and women, but you can definitely expect resistance, so take heart in the fact that if you are persecuted for righteousness’ sake, and “If you are insulted for the name of Christ, you are blessed, because the Spirit of glory and of God rests upon you” (1st Pet 4:14). Now who wouldn’t want that!?
Take a look at this article: What Does the Bible Say About Criticism? 
Resource – Scripture quotations are from The Holy Bible, English Standard Version® (ESV®), copyright © 2001 by Crossway, a publishing ministry of Good News Publishers. Used by permission. All rights reserved. [1.] Mill, John Stuart (1859). “Introductory”. On Liberty (4th ed.). London: Longman, Roberts & Green (published 1869). para. 5. [2.] The European Convention on Human Rights guarantees the right of freedom of expression (Article 10).