The reason for this can be gleaned from two statements that Lynn has made in the past. The first statement that hints at why strangers are scary and bad and not trustworthy is the "Please, please, PLEASE love Anthony" letter. As we all know, the main selling point for Anthony is that John and Elly know who he is and what to expect from him. Even if they do have their reservations about his character, they would far rather Liz get married to a boring, selfish, unambitious git they know than a good man who they don't. They can predict what Anthony will do in any given situation so the familiarity of his having a certain amount of wanderlust and treating Liz like a maid, cook and nanny is more reassuring than being treated with respect and devotion by someone they've never met could ever be. They aren't familiar with him so they can't predict what he'll do so they're scared of him.
We also have to contend with a Lynnsight in which Lynn talked about how she felt as if her children were almost strangers to her because she didn't grow up knowing them. Having to get to know these odd little people that insist on trying to get her attention seems to have scared the crap out of her. Much like Dr Seuss, she seems to have spent most of her time with them in a cold sweat wondering what bizarre and horrible thing they might say, do or ask of her. Worse still, she couldn't avoid these scary, scary strange people she couldn't understand.
This is yet another reason why Lynn impresses me as having never really grown up much mentally. The same sort of rigid, infantile thinking that prevents her from accepting criticism also keeps her from seeing that a stranger isn't necessarily always a threat.