As we see there are 2 meanings of “so-called” that can be confused or misinterpreted, of which one implies falsehood and the other doesn’t.
One. to show that something or someone is commonly designated by the name or term specified.
“Western Countries belonging to the so-called Paris club”
Two. used to express one’s view that such a name or term is inappropriate.
“she could trust him more than any of her so-called friends”
Since so-called I feel is very often used to suggest that a title for something describes a meaning that isn’t necessarily accurate, what’s another term that simply expresses that something is titled something without judgment of the title?
You're right, but the "so-called" only becomes suspicious when it's included unnecessarily.
From OPs example if you just omit it the sentence is fine and doesn't imply that the friends are not actually friends.
In the first type of usage, "so-called" provides information that the reader is unaware of, so it's use does not imply the name is inappropriate.
In the second type of usage it's presumed the reader already knows the name, inserting "so-called" emphasises that the subject has whatever name.