Here are some examples:
Near the end of his life, the prophet Lehi addresses his children saying, “I desire that ye should remember to observe the statutes and the judgments of the Lord; behold, this hath been the anxiety of my soul from the beginning.” (2 Nephi 1:16, emphasis added)
The prophet Jacob explains how he was able to receive revelation for his people. “For because of faith and great anxiety, it truly had been made manifest unto us concerning our people, what things should happen unto them.” (Jacob 1:5, emphasis added)
When the prophet Alma taught the people of Ammonihah, he told them, “My brethren, I wish from the inmost part of my heart, yea, with great anxiety even unto pain, that ye would hearken unto my words, and cast off your sins, and not procrastinate the day of your repentance;” (Alma 13:27 emphasis added)
The word “anxiety” always has to do with someone being so faithful and considerate that they became anxious over the people they love. To me, I felt that Heavenly Father was telling me through these scriptures that having anxiety is not always a bad thing.
Having fear can mean that you are cautious, caring of other people’s feelings, think before you speak, etc. Think about the opposite of those things: having no fear would make a person thoughtless, neglectful, loose-tongued, etc.
Anxiety is a loving attribute of a parent. My mom has shown me to be scared when I see young children with their fingers too close to a door where they can get smashed. My parents taught me to have fear when driving a car, in order not to cause anyone unnecessary harm. Even now, though I am grown up and live a state away, my parents still let me know how much they worry about me and are willing to help me with anything. Through their anxiety, my family has shown me how much they love me.
Heavenly Father and His Son Jesus Christ have given me people who are anxious about my well-being, as well as people who I anxiously love. They give me people to love so that I can imagine how much They love me.