What is the biblical basis for allowing atheists to speak openly and freely in society?

On basic human psychology

Censoring someone doesn't change their beliefs; it just prevents them from expressing those beliefs where they will be caught. However, censoring someone will absolutely harden their heart against you. As someone who grew up atheist, I can absolutely tell you that I would have spent my entire young adult life in prison, protesting against such discrimination, and I would not have converted.

A change of heart does not occur in the face of force, but with love. Further, a change in behavior does not mean that a change of heart has occurred, but a change of heart will always result in a change of behavior.

On finding lost sheep

John 21:15
When they had finished eating, Jesus said to Simon Peter, “Simon son of John, do you love me more than these?”

"Yes, Lord," he said, "you know that I love you."

Jesus said, "Feed my lambs."

Romans 10:14
How, then, can they call on the one they have not believed in? And how can they believe in the one of whom they have not heard? And how can they hear without someone preaching to them?

If our goal is to convert as many people as possible to Christianity, one of the first steps has to be to find the non-believers. When I was in college, this was really easy: put up fliers for a Christian event, and you would be accosted. Give out free coffee on a cold day in the name of our Lord, and you would be accosted. My most productive conversations with non-believers occurred during interactions like this. But what if it was literally illegal to express their views to me? Those interactions would never have occurred, and there would be fewer Christians today.

What would Jesus do?

Usually, when trying to find out what Jesus would do in a particular situation, we have to get abstract about his character and nature. This is not the case now; we know exactly what Jesus would do:

1. Find the sinners.
2. Engage the sinners in dialog.
3. Engage in very public dialog with anyone and everyone, especially sinners.
4. Eat with the sinners.
5. Feed the sinners.
6. Heal the sinners.
7. Perform miracles for the sinners.
8. Save the sinners from being stoned to death.
9. Get accused of being a sinner by associating so much with them.
10. Die for their sins.
11. Forgive those who killed him as they were killing him.
12. Conquer death.

(If necessary, I can chase down all the verses for those, but I shouldn't think it necessary.)

Jesus was all about engaging in very public dialog with people who were spiritually lost. At no point in the Bible does he try to censor anyone.

Samaria

Acts 1:8
"...you will be my witnesses in Jerusalem, and in all Judea and Samaria, and to the ends of the earth."

John 4:9
For Jews do not associate with Samaritans.
Alternate: For Jews do not use dishes Samaritans have used.

On first reading of Acts, it seems odd that Jesus specifically mentions they have to witness in Samaria. But, in John we learn that Jews were extremely prejudiced against the Samaritans, to the point where they refused to even share dishes. In the ancient world, when Jews made their pilgrimage to Jerusalem, they would travel miles and miles out of their way just to avoid Samaria. In Acts, Jesus is essentially anticipating an argument. "The Lord said to the ends of the earth, but he surely didn't mean also those dirty Samaritans." Yes, we must love even our enemies (Matthew 5:44). Censorship is about as unloving as one can get short of physical violence.

Witnesses, not enforcers

Acts 1:8 also tells us our role, which we can also see in the Great Commission:

Matthew 18:19-20
"Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, and teaching them to obey everything I have commanded you."

We are to be witnesses, disciplers, baptizers, and teachers. We are not enforcers of God's law. We are not judges. And even if we were, the only instance of censorship I remember from the Bible is when God ordered Joshua and the Israelites to kill every man, woman, child, and domesticated animal in Canaan who wasn't an Israelite because their pagan beliefs would corrupt the Israelites, and I'm pretty sure everyone can agree that we are not called to genocide.

Paul in Athens

Selections from Acts 17:22-34
22 Paul then stood up in the meeting of the Areopagus and said: "People of Athens! I see that in every way you are very religious. 23 For as I walked around and looked carefully at your objects of worship, I even found an altar with this inscription: to an unknown god. So you are ignorant of the very thing you worship—and this is what I am going to proclaim to you.

24 "The God who made the world and everything in it is the Lord of heaven and earth and does not live in temples built by human hands. 28 'For in him we live and move and have our being.' As some of your own poets have said, 'We are his offspring.'

29 "Therefore since we are God's offspring, we should not think that the divine being is like gold or silver or stone—an image made by human design and skill."

32 When they heard about the resurrection of the dead, some of them sneered, but others said, "We want to hear you again on this subject." 33 At that, Paul left the Council. 34 Some of the people became followers of Paul and believed.

-1 And then Paul and his followers destroyed all the pagan altars in the city.

Clearly, that last line is not in the Bible. Paul was: courteous regarding their beliefs ("I see that in every way you are very religious"); firm in his own convictions; and in a public debate with non-believers. After stating his position, some people sneered, and he let them. He converted those he could, taught them what he could, but recognized that it was not his responsibility to try and force anyone into a change of heart, or to censor them in any way.

Matthew 10:14
If anyone will not welcome you or listen to your words, leave that home or town and shake the dust off your feet.