Not knowing what the website is it hard to say what the problem is, post only the domain name link not the http/www etc.
A screenshot of the Avast Alert window, with the More Details option expanded will help.
Trustworthy sites can be hacked also.
I don't know how the alert would occur if you have the Web Shield disabled, which is why the screenshot will help.
Are you using the Avast Online Security browser add-on (completely independent of the avast program, could it be this I wonder) ?