What if your server wants chmod to be 777?

I’ve just found out that a server I am working on really wants chmod to be set to 777, on quite a lot of WordPress files. This feels very unsafe to me, but there is simply no way around it.
I am now wondering: what are the risks when I do this?
Is it sufficient when the admin-user has a non-standard username and non-standard password or do I need to do more to keep the site safe?

I’ve noticed it’s impossible to update plug-ins and wordpress itself when permissions aren’t set to 777 for files in wp-admin, so the only solution I can think of now is to set them to 777 temporarily and after the updates set them back to 755 and 644.