I do see the term "dead" in that and many other texts.
You pointed out that Jesus told a man who wanted to bury his Father before following Jesus, "Leave the dead to bury their own dead."
So what does dead mean in this verse?
Jesus seems to imply that this man, if he gave up his attachment to his earthly treasures and started to walk with Jesus, that man would not be one of the dead who were about to bury his father, but he would be living. Jesus elsewhere, in John 6, says that coming to Jesus to hear His teaching is doing the work God requires in order that we believe Jesus teaching, and so believe and keep on believing in Jesus.
I am translating the greek verbs (indicatives, infinitives and subjunctives) and participles here to capture their essential senses snd show what I see Jesus saying in the Greek text.
27. Do not keep on labouring for the food which perishes, but for the food that endures to aeonous life, which the Son of man will give to you; for on Him has God the Father set His seal... 29 This is the work of God so that (hina, not hoti) you might keep on believing (pisteuEte: Present active subjunctive) in Him whom He sent. (The work God requires of these contemporaries of Jesus is to put effort into getting close enough to Jesus to hear his teaching and observe His signs in the hope that they will believe the words and signs and put their faith in Him and keep on believing in Him. Why does God want them to keep on believing in Jesus?
35 I am the bread of life; he who comes to me shall not hunger, and he who believes in me shall never thirst...
Jesus is the bread that gives life to men so that they won't die. Those who ate Moses' bread eventually died. Those who eat Jesus will not die.
39. and this is the will of Him who sent Me, that I should not start to lose anything of all he has given me, but start to raise it up on the last day. 40 For this is the will of my Father, that (hoti, not hina) every one who continues seeing the Son and continues believing in Him should keep on having aeonous life. and I will raise him up at the last day.
(Those who keep their eyes on Jesus and keep on trusting Him will keep on experiencing the kind of life that pertains to the age to come, and will physically come to life during the last 1000 year day of this creation.)
44. No one is able to start coming to Me unless the Father who sent Me starts to draw him; and I will raise Him up on the last day.
(This is spoken to Jesus' contemporaries about the work of the Father before Jesus is lifted up in attracting Jesus' contemporaries to seek out Jesus. After his crucifixion and resurrection Jesus does the drawing to Himself. God has initiated Jesus' contemporaries interest in Him through the signs and controversial teaching He is expressing through the Lord. Jesus had no form or comeliness that anyone would be attracted to Him, had not the Father have piqued their interest with signs and controversial teaching.
The text does not say Jesus will not be raising up those who are not coming to Him during His ministry. Jesus will raise up those in his audience who have come to Him on the last 1000 year day: either at the beginning as a transformed saint, or at the end to be judged as an unrepentant sinner. But He will also raise up those not coming to Him during His ministry. A day is coming when ALL in the graves will hear His voice and come forth. Jesus' point to these people here is that He will be raising them and judging them on the last day, so they need to be careful how they hear, and about what they do with Jesus.)
47. Truly, truly I am saying to you, the one continuing believing has aeonous life.
(Trusting Jesus is the kind of life that will be enjoyed by those resurrected into the coming age, and those doing it now, have that life now. They know God and Jesus Christ even now.)
48 I am the bread of life.
(Jesus is the bread that gives life.)
50 This is the bread which comes down from heaven, that a man may start eating of it and might not end up dying.
(If we start absorbing Jesus, we have the possibility of not dying. Jesus does not say , "that if a man may start eating of it, he will not die.
51 I am the living bread which came down from heaven; if anyone starts eating of this bread, he will live into the age (eis ton aiOna) , and the bread which I shall give for the life of the world is my flesh.
(But here Jesus says that if anyone starts absorbing Him, they will live into the age. So here there seems to be some assurance of being raised at the beginning of the 1000 year last day. Here, Jesus identifies the bread as His physical body. He says He will give it. for the world. Maybe he means he is going to surrendering His body to be broken, so that the world may have access through the veil of His flesh into the presence of God.)
53 Truly, truly I am saying to you, unless you start eating the flesh of the Son of man and start drinking His blood, you have no life in you.
(You have no life in you, means you are dead. So, perhaps dead means without Jesus inside you?)
54. He eating my flesh and drinking my blood has aeonous life, and I will raise him up at the last day.
(The ongoing process of absorbing Jesus' flesh and blood is the same as having aeonous life. John 17:3 says knowing God and Jesus, being in a living relationship with them, is aeonous life. Jesus said once "My food is to do the will of Him who sent Me." So, our food would be to do the will of Jesus. To eat for Jesus was to do the Father's will., to embody the Father. To eat for us could be to do Jesus' will, to embody Jesus. This could be to eat His flesh, to do the Word of God. But it is possible to do God's Word in the wrong spirit., without love. Drinking Jesus blood could be embodying God's Spirit: walking in the Spirit.)
55 For my flesh is food indeed, and my blood is drink indeed. 56 He eating my flesh and drinking my blood is abiding in me, and I in Him.
(So maybe walking in Jesus' Word and walking in Jesus Spirit is to abide in Him and He in us.
57. As the living Father sent Me, and I am living because of the Father, so he eating Me will live because of Me.
(As Jesus walked in the Father's word and walked in the Father's Spirit, He had life. As we walk in Jesus' word and Jesus' Spirit, we will live.)
58 This is the bread which came down from heaven, not such that the fathers ate and died; he eating this bread will live into the age.
(Walking in accord with Jesus' word will give one entry into the first resurrection and the age to come.
63 It is the Spirit giving life, the flesh is profiting nothing; the words that I have spoken to you are spirit and life.
(But doing the Word without doing it in love profits nothing. The words Jesus spoke were the will of the Father spoken in love; they were therefore spirit and life.)
What does "leave the dead" mean, then? The dead here are those who are not doing Jesus' words in love. The physically dead body is also not doing the words of Jesus in love. "Leave those not doing my words to bury those in their household who are also not doing my words. As for you, follow me. Put yourself in a position to learn my will and to do my words so that you will be living."
So someone using the term "spiritually dead" who does not mean "not doing the word of God in love" needs to find a text or passage that teaches their meaning of the term. They should not load the term with unbiblical baggage and expect others to accept their meaning is biblical.