What you need to consider:
HK never was a cheap/easy place to live in with 4 kids. Since you ask the question, I can only assume you are not speaking Cantonese and you will likely want to have you kids at an international school, and those are crazy expensive here. With that said, since protest started, I see a lot of expat leaving HK (contradicting some posters here), meaning that at least there will be more seats available in those schools (if those schools do not run in trouble to find teachers that is…), but that also means that tuition will only get higher, not lower. So be prepared for that.
HK economy wasn't in very good state before the protests, and it took a serious toll since then. You have to consider that if you are moving in here, you will likely be on a work visa, meaning: "bound to one employer", how is that employer going to handle the current crisis/recession? How financially sound/stable is this employer, and what are their long term plans in HK?
If your plan is to move here to then find new opportunities, do bear in mind that the economy is now in recession, less opportunities are available, and depending on your industry you will have to compete with more local candidates who 1) don't need a visa, 2) take a much lower pay, 3) are already local and generally easier to work with for local companies (even foreign companies HR favor local over expats for many reasons). Generally speaking, projects and new hires are mostly frozen for now and until further notices.
Accommodation is notoriously very expensive in Hong Kong, and a family of 4 will require quite a large housing (so even more expensive). While I do tend to see more restraint in the rental being suddenly increased by landlords these days (yes, this is a real thing in HK, they can and will increase heavily the rental after the first year or so…), I also don't see a dramatic decrease in rental around here… This may change with the protests, as more and more foreigners (including mainlanders) move out of the city, since their presence here is one of the driving force of housing price inflation… (albeit, not the only one)…
From a safety point of view, here again, it will depend on where you live, where you are from, and what you will do in here… it's anyone's guess what the situation will be tomorrow, let alone in 6 months time… If I base my assumptions on today's situation, as long as you don't partake in any protest, don't go near them, don't voice too much your discontent about situation here, and don't need to cross an angry mob for any reason (including police), you should be safe… but any of this can change very quickly… (For instance, I was called by the school to go fetch my kids because police were throwing tear gases nearby, and had to cross both rioters&police on a bike to fetch my kids around there because transports&roads were being blocked, it was only once, and I did not suffer more inconvenience than that, but it could have been much worse)…
Another thing to consider here is the environment you want your kids to grow in… HK is getting more and more influenced/controlled by China government, the "freedom" enjoyed is getting more and more restrained, and the trend is very unlikely to reverse at this point… China is committed to strengthen their grasp on HK, putting indoctrination to a next level… (examples of this include the currently-still-being-discussed obligation for schools to sing the Chinese anthem, even for foreign schools, and the "sanctuarization" of the anthem, making it a legal offence to alter/joke/discuss the anthem for kids, who then face legal consequences, including jail time… this is just one example in a very long list here…).
The point is that the overall environment is getting more and more like a police state, with heavy control of both media and education (indoctrination by the CCP). This is clearly a goal of the BJ government and will not be soften in any way in the coming years (just look at the news where CCP vows to increase patriotism in education, and "fix" the hong kong legal system…).
I am not saying you can not live happy in this kind of environment, some definitely do, I am merely pointing that this is, indeed, such an environment… How well you will do in this entirely depend on you…
With all those negative aspects mentioned (and the list can go on), HK still retains a lot of good points (low taxes, - at least for now - great education, perfect location in Asia for accessing Asia, opportunities to access Chinese Markets for companies, reasonably westernized life style, etc…).
I hope that help.