I think it sounds like you have the best of intentions OP. You said you think your friend is overwhelemed and doesn't know where to start so maybe tactfully suggesting ways you could help to begin to tackle it with her might be a good port of call.
I do think there is a big difference between messy and cluttered and unsanitary and unhygeinic when it comes to how people live. Some people would hate to live in a messy cluttered house but I don't think that can be said to be a neglect issue as such. A house which is unsanitary though? That is different and it can point to neglect issues for the children..even if the parent loves them and is trying and so on.
I've been in this situation and it was really bad. I'm in no way a clean freak..I tend to spread mess wherever I go, but was shocked at this particular persons house. Their child had rotting food hidden in the bedroom, there was fresh and stale cat urine in all the rooms and the kitchen had not been cleaned properly for a long time. Basic washing up but the rest just left. Even things such as mouldy towels used in boots of the car for swimming..never taken out and cleaned..never smelt anytihng like it in my life. Awful. Myself and another person did try to help with cleaning (they did more cleaning than me) and encouraging at least to clean things like litter trays..but it made little difference. In the end other person took piles and piles of washing from the floor of this persons bedroom that had been there for a long time and spent hours in a laundrette washing them..said they all smelt of cat wee. Whenever we came home from that persons house we had to put our clothes straight in the wash..just peel them off at the door as we smelt like cat pee. 
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It was doubly sad because that person pretty much ignored their child much of the time or if they did pay attention shouted and yelled and told them to shut up and so on. One time I was even offered the last of a hot dinner instead of the child (I refused and gave my piece to the child). That child was also unkempt, hadn't seen a dentist regularly, clothes which didn't fit and smelled awful, didn't wash very often..I dread to think what she went through at school. I wanted to report to social services at one point but apparently that had already been done more than once..with the predictable response that it was clearly malicious and done with the intention of screwing with this person rather than concern. So I felt it was more worth trying to assist with things like mental health, parenting and so on where I could (I was massively depressed myself at the time). I still feel guilty I never did report at times..I have no contact anymore so I don't know the current situation. I wish I had done more when I was aware of it more fully.
In that case I think just dismissing all of that as not having the same standards of hygeine would be a big mistake. I also think that even without the added way that I could witness the child was being treated emotionally the house itself and lack of hygeinic and healthy or adequate food was an indication of neglect and needed intervention.
So to go back to your friend OP I think that she needs help and fast. I think that it is so so hard to know what to do or say. I never had a proper frank discussion in the situation I describe..I tried to be as tactful and diplomatic as possible - we all did. But it was like the elephant in the room you know? And the child did suffer..as will the children at your friends house if it is in that much of a state, no matter how she is with them on an emotional level.