I think that if somebody wants to be called they, you should call him or her they. Similarly, if they want to be called he (or she) you should call them he (or she). It's common courtesy, like calling somebody who doesn't like his given name Jim rather than James (not to mention calling [untypable symbol] the artist formerly known as Prince). And I expect many people would not be happy about being called they.
Most of the OP's examples are specific people that the speaker knows, and for whom also the speaker would presumably know which pronoun they prefer (father, girlfriend, teacher). In these cases, the speaker should use the person's preferred pronoun (probably he, she, he, respectively). Furthermore, it's confusing to use they for an obviously female dog, and there's no reason to since the dog doesn't have feelings.
Nowadays, it's permissible to use they for an unknown person of a specific gender (for example, "somebody left their ring in the ladies' room").
Let me explain the way the grammar used to work, at least for me. Traditionally, prescriptivists said that singular they was ungrammatical. Some people never used it all. I grew up using it, and I know the rules I grew up with, but people who grew up speaking other dialects may have had different rules.
Now that non-traditionally gendered people have appropriated they, the rules are changing.
In the grammar of singular they that I grew up using, you could singular use they only for a person whose gender was unknown, and only for unnamed antecedents. So
*Leslie called; they want you to call them back,
was ungrammatical, but
Somebody named Leslie called; they want you to call them back,
Similarly, you could have had the following conversation.
"The electrician came today."
"What did they say needed to be fixed?"
"She said that we need a new breaker panel, and it will cost six hundred dollars.
You needed "she" (or "he") in the third line because the first speaker has met the plumber, and presumably knows their gender.
So, even according to the old rules, it was ungrammatical to use they for antecedents like "that man selling balloons", "Jack", etc.
According to the new rules, it may be possible to use it for an unknown person of a known gender. See this Language Log post. But we still don't use it for a specific person of known gender unless they want to be referred to by the pronoun they.