I wouldn't trust a VanitySearch site that isn't made by me or WhyFy.
The issue is more about who creates the site rather than what is used to create it.
It will be difficult for me to know who I can trust. Just a small search, I can get many search results related to Vanity Search. Most of them are open source on Github. I can't even tell which one is safe or not. It is possible to scan the file before installing, but there might still be vulnerabilities like this subject, right?
I can tell you who not to trust.
You should never trust a website, even if it is popular. For example you should never trust bitaddress.org website even though it is a popular project. Because it is a website and you can't tell what really is happening when you generate a key there.
You should also never trust a Vanity address creator that generates the key on their own. There is nothing stopping them from saving the key. There was ways to make this safe by just giving them a public key and they work from there but there are some complications involved.
And finally being open source and on Github doesn't mean they are safe. Being that and popular to have their code reviewed by others makes them safe.