So if you are looking for new business leads, in a different sector or if you are not concerned about where they come from, you take a more liberal approach. In this way, you may pick up interest from distant, unanticipated connections. However, if you want to develop an exclusive or defined set of connections, you would be inclined to stick to the criteria you set out.

I tend to opt for people who I think I might do business with or with whom I have some degree of familiarity. I am deeply antipathetic to those who don’t personalise, often being slow to reply and then (usually) with a personal note! I have to confess that if I am sure I don’t wish to connect, for whatever reason, I take the easy option and ignore the invitation. It’s highly unlikely to be from someone who had made the effort to contact ME.

As for offence being taken, I doubt it – probably more ” I wonder why not???” Especially as I suspect your courteous approach is unusual. People are probably much more likely to ignore an invitation, as I do.
Maybe we need to be more mindful of the impact of not connecting, however we do it – after all, it’s still sending a message. We need to consider whether it is the one we want.