The Online Safety Bill needs "radical amendments" to prevent it "trampling" on free speech, The Christian Institute has said.
It has called the government's approach to online safety "incredibly dangerous" and "undemocratic".
The organisation warns that the Bill "will hand weapons to government ministers to silence views they disagree with and apply strong commercial pressure to Big Tech executives to do the same".
"It risks the most draconian censorship of ideas on the internet in the Western world," The Christian Institute said.
It welcomes measures aimed at addressing illegal content and protecting children, but says changes are needed to protect free speech.
"Freedom of speech is under attack today," it said.
"Many activists take the view that 'you can say anything we like'! The only opinions they want in the public square are their own. Although well-intentioned, this Online Safety Bill will hand weapons to these thin-skinned activists to silence their opponents.
"These powers handed to Government ministers to decide what you can and cannot say on the internet are outrageous and undemocratic.
"Ministers will be able to change the law with minimal parliamentary scrutiny, creating the risk of politically-motivated bans on what you can say on the internet."
MPs will debate the Bill for the first time on 19 April. The Bill proposes fines of up to 10 per cent of global revenue on tech companies that fail to take action against "legal but harmful" content on their platforms.
Responsibility for regulating online safety will fall to communications regulator Ofcom, which is to be given new powers under the proposals.
The Christian Institute said the Bill as it currently stands risks silencing those with unpopular views, including Christians.
"This vague notion of restricting content deemed 'legal but harmful to adults' will encourage Big Tech's worst instincts. Most of Silicon Valley shares a very clear social and political agenda," it said.
"They already promote ideas they like and downgrade those they don't. This Bill will make that even worse.
"It actually incentivises activists to complain to social media companies about opinions they don't like. The 'risk assessment' duties in the Bill mean tech companies will have to be seen to respond to these complaints, even if they are bogus and politically-motivated.
"And the Bill makes clear that their terms and conditions can be as restrictive as they like, as long as they're applied consistently.
"Mainstream Christian beliefs are already being cynically attacked as 'harmful' by activists intent on silencing them. The Government should be standing up to these bullies, not giving them a stick to beat us with.
"Free speech in the UK should not be decided by Silicon Valley executives. And government ministers should not be able to bring in laws censoring speech without Parliament having the opportunity to amend them."
