as parent to a 4 month old that refuses to sleep at all during the day and by 7pm has got so tired she has crying fits yet still fights it and can go on until around 11 (when she then drops off and sleeps through to 6-8am, which is great) I sympathise alot, I am in a similar situation, get home from work, screaming baby, and its hard. Big differnce being she is my kid so I have that bond and I have some control over my situation and we have now learned how to manage her and stop her crying at least for half hour to hour periods until the 'tantrum' passes and she nods off
There could be any number of reasons, colic (can be awful, we found Dr Browns anti colic bottles and a proper burping routine works great), teething (Ashton and Parsons powder), a deeper medical condition, to just needing attention. No one can really give you any advise as we have no idea on the child's or parents situation, are they the type that might just switch off and ignore their crying baby?
We also dont know your relation with your neighbours? If your on pretty good speaking terms then maybe a passing concerned comment may help? Do you have kids yourself may they see you as someone that could maybe give some advice to them?
Like you say there is a risk of stressing them out if you mention anything, but equally they could also be at their wits end themselves and desperate for any advise
the only thing I can really say is that in my experience when it gets to that demented hoarse yelling stage it is something quite wrong, be it extreme tiredness, hunger or discomfort from colic / teathing or whatever, the baby isnt crying for a trivial reason