Is it true that any one can set up a website for fundraising without declaring a legal entity?
For example, my church needs to raise fund for repair work, the project would cost about $40K. If I want to create a website for people to send me money for that cause, do I have to declare a business?
There's nothing that makes it illegal to ask others to give you money to donate to a third party.
But if you want to say you're fundraising on behalf of another organization, obviously you need its permission. And if you want contributions to be considered charitable for tax purposes, and you want to make sure you don't wind up paying taxes on contributions "sent to" you but then passed on, then you may need to start worrying about a separate entity.
It would be more straightforward to offer to create, host and administer the website for the church, with it receiving the contributions directly.
Churches are available for tax-exempt status, and if your church is filed this way then you should work with them to determine how you will legally transfer money in this tax-exempt manner.
Donors (or many of them) will likely be interested in receiving a tax letter than they can claim for write-offs at year-end. You, not being an officer or representative of the legal entity that is the church, cannot write this letter and will need to coordinate with the Church officers to have them write said letters.
I think you can do all of this informally. People can give you money and trust that you'll be honorable with it. You need transparency regarding online processing fees, and their actual total donation.
You expose yourself to suit if someone claims malfeasance. No entity has obligation to support nor represent you in this regard. I cannot cite and fiduciary laws here – I am just giving general guidance.
In general, it's probably better that you have some written agreement with the Church stating your intent and obligations, and their intent and obligations, in the relationship with you.