Everyone has a different view and approach on this topic. It's tough.
Regarding to cyber security of websites, there is a saying in the industry: It's not a matter of "if", but a matter of "when" a website will be hacked. And it's likely that the website has already been hacked.
I've resigned myself to the fact that I'm easily found on the internet. I work in high-tech. I have done public speaking. I've had videos taken of me giving a presentation. It's just a fact of life.
Regarding genealogy and family information, if someone is persistent enough, it is not out of the realm of possibility that they will be able to find out some info about you. There are also enough publicly available records, in enough places, that it is near impossible to scrub the internet.
As to identity theft, all credit card companies have made it easy to deal with this situation and get your situation restored. Again, it's not a matter of 'if', but 'when'. Yes, it's inconvenient. But with some simple precautions (like keeping a regular eye on your accounts) it's not the end of the world.
Given all of this, I'm a bit sanguine about it. Would it be great if the situation were different? Yes, absolutely. But the United States and corporations there absolutely hate for people to have privacy. Europe has GDPR, which is a start. California now has some privacy laws in place. None of these laws are perfect. And companies do not always follow the laws. I know, because I've been on the other side of the fence in a company that had to deal with GDPR when it came out. These laws are incredibly difficult to follow and enforce.
So, I've kind of given up being paranoid about the situation and I try to look at the situation from a risk evaluation / management situation. What are the risks? Prioritize the risks. Have a mitigation plan where I can.
This also includes people who reach out in different ways. So they tried to contact you via LinkedIn. Are you interested in having a conversation with them? If not, then you can block said person on LinkedIn and they can no longer contact you. The same can be done on almost all social media sites. Likely they will go away. If they don't then there are standard escalation paths that anyone can follow.
By the same token, how much would it hurt to at least find out what they have to say? If it's a reasonable conversation, then it might be interesting. If it gets weird, then there are alternative routes discussed above.
These are just some possibilities and ways of looking at the situation. As I said, everyone has their own viewpoints.