SEPARATION ANXIETY & STRANGER ANXIETY: WHAT TO DO?!
Let's start with defining what these two phenomena are:
Stranger Anxiety is at play when your child reacts negatively to a face they "perceive" to be new. We put that in quotes because their capacity for recalling familiar faces is still developing, so even if it is someone they have already met, they may not remember exactly who they are.
Separation Anxiety occurs when your baby learns that Mom and Dad still exist even if they can't see them--the concept is called object permanence and is actually a pretty cool mental leap; this is coupled with their understanding of cause and effect. For example, they realize that a loud yell often brings them back. It can be frustrating to feel like you can't leave your baby without them getting upset, but it is a sign of good bonding between you, AND it is the start of them starting to build coping mechanisms by holding healthy boundaries around their upset.
"How?" you may ask. We will get to that but first, let's nerd out for a moment.
What's behind these phenomena?
All very healthy cognitively
Effects some babies more than others
Can be very frustrating for parents
Concept of "object permanence," which is an important milestone– Peekaboo helps develop this understanding
Part of it is Nature, we all have a certain amount of "alarm hormones" that help us survive, and if you are generally a more anxious parent, odds are you will have a more anxious baby
Part of it is Nurture; if you are anxious about leaving your baby or having them around a particular person, your baby will pick up on it and behave accordingly. Babies watch caretakers for cues.
Goal is to find ways to curb anxiety
What you can do (Generally)
Remember that fears keep children safe (e.g., fear of falling downstairs, fear of strangers)
Not healthy to discourage the development of fears
Goal is to instill a feeling of security in them and provide them with a context for these fears so they can recognize when they are safe and don't need to be scared
Usually, by 2-3 (often sooner), children are capable of thinking more rationally, and some of the anxiety will fade
Respect the child's feelings
Be reassuring