I have only read the samples of the book provided by Amazon and Google, so I cannot adequately state Shedinger's argument. However it seems that he defines both Islam and early Christianity as "social justice movements":
I came to the conclusion that [Islam] was a social justice movement and I think that's who Jesus was in the first century so I conclude Jesus is more like a Muslim.
On that basis, Jesus was doing the same thing that Muslims are called to do. If that argument sits well with you (and it does not with me), it's possible to answer, as Shedinger does, with a "very qualified yes".
The most awkward portion of the question arises from fact that Jesus was born more than half a century before Muhammad. Therefore, if the claim that Jesus was a Muslim is true, it ought not be confused with the usual understanding of Muslim given by Wikipedia:
an adherent of Islam, a monotheistic Abrahamic religion based on the Qur'an—which Muslims consider the verbatim word of God as revealed to prophet Muhammad—and, with lesser authority than the Qur'an, the teachings and practices of Muhammad as recorded in traditional accounts, called hadith.
Certainly Jesus did not practice the Five Pillars of Islam:
Jesus said to him, "I am the way, and the truth, and the life. No one comes to the Father except through me."—John 14:6 (ESV)
Jesus told his followers to pray, but not in the precise manner of Islamic prayer:
[Jesus said,] "And when you pray, you must not be like the hypocrites. For they love to stand and pray in the synagogues and at the street corners, that they may be seen by others. Truly, I say to you, they have received their reward. But when you pray, go into your room and shut the door and pray to your Father who is in secret. And your Father who sees in secret will reward you.
"And when you pray, do not heap up empty phrases as the Gentiles do, for they think that they will be heard for their many words. Do not be like them, for your Father knows what you need before you ask him."—Matthew 6:5-8 (ESV)
To be clear, I don't mean that Islamic prayer is hypocritical or "empty phrases". Nor did Jesus mean here that corporate and standardized prayer is wrong (he gives a formula for corporate prayer immediately after the above passage). Rather, Jesus did not make five-times-daily prayer and the details of how it is performed a priority.
Again, charitable giving was one of the things Jesus told his followers to do. But he did not hold to 2.5%:
But woe to you Pharisees! For you tithe [or give 10% of] mint and rue and every herb, and neglect justice and the love of God. These you ought to have done, without neglecting the others.—Luke 11:42 (ESV)
Jesus did fast (famously for 40 days and nights while being tempted by the enemy), but he did not require his followers to fast:
Now John's disciples and the Pharisees were fasting. And people came and said to him, "Why do John's disciples and the disciples of the Pharisees fast, but your disciples do not fast?" And Jesus said to them, "Can the wedding guests fast while the bridegroom is with them? As long as they have the bridegroom with them, they cannot fast. The days will come when the bridegroom is taken away from them, and then they will fast in that day."—Mark 2:18-20 (ESV)
Jesus never traveled to Mecca. He was taken as far south as Egypt as a child and walked as far north as Saïda as an adult, but never ventured much further east than the Jordan River. He did routinely visit Jerusalem and, of course, was crucified there. But there's no evidence he even knew that Mecca existed.
On the other hand, Jesus would fit the secondary meaning given by Wikipedia:
"Muslim" is an Arabic word meaning "one who submits to God".
Christianity's first great philosopher, Paul of Tarsus, wrote:
Have this mind among yourselves, which is yours in Christ Jesus, who, though he was in the form of God, did not count equality with God a thing to be grasped, but emptied himself, by taking the form of a servant, being born in the likeness of men. And being found in human form, he humbled himself by becoming obedient to the point of death, even death on a cross.—Philippians 2:5-8 (ESV)
Christians believe on the basis of the earliest historical accounts of Jesus and the movement he founded, that Jesus submitted to God's will to an extant that has never, and can never, be duplicated. Yes, Jesus called for a radical commitment to social justice. But he also called for holiness, self-sacrifice, devotion to God, humility, and acts of love toward both God and other people. He was, in this limited sense, Muslim par excellence.