"What a contrast between His teaching in regard to the new kingdom and that which they had heard from their elder! Jesus had said nothing of delivering them from the Romans. They had heard of His miracles, and had hoped that His power would be exercised for their advantage, but they had seen no indication of such purpose. DA 238.1"
"When Jesus therefore perceived that they would come and take him by force, to make him a king, he departed again into a mountain himself alone."
Both passages deal with the expectation that Jesus would be a political/earthly king. John 6:15 describes the people wanting to force Jesus to be king, while EGW describes the disciples' disappointment that Jesus wasn't delivering them from the Romans.
"As they opened the door to doubt, their hearts became so much the harder for having been momentarily softened. Satan was determined that blind eyes should not that day be opened, nor souls bound in slavery be set at liberty. With intense energy he worked to fasten them in unbelief. They made no account of the sign already given, when they had been stirred by the conviction that it was their Redeemer who addressed them. DA 238.2"
"In whom the god of this world hath blinded the minds of them which believe not, lest the light of the glorious gospel of Christ, who is the image of God, should shine unto them."
Both passages discuss the blinding influence of Satan that prevents people from accepting the truth. The EGW passage describes the people's hearts hardening due to doubt, while the Bible verse speaks of Satan blinding the minds of unbelievers. The thematic connection is strong.
"But Jesus now gave them an evidence of His divinity by revealing their secret thoughts. “He said unto them, Doubtless ye will say unto Me this parable, Physician, heal thyself: whatsoever we have heard done at Capernaum, do also here in Thine own country. And He said, Verily I say unto you, No prophet is acceptable in his own country. But of a truth I say unto you, There were many widows in Israel in the days of Elijah, when the heaven was shut up three years and six months, when there came a great famine over all the land; and unto none of them was Elijah sent, but only to Zarephath, in the land of Sidon, unto a woman that was a widow. And there were many lepers in Israel in the time of Elisha the prophet; and none of them was cleansed, but only Naaman, the Syrian.” Luke 4:23-27 , R. V. DA 238.3"
"And he said, Verily I say unto you, No prophet is accepted in his own country."
The EGW passage directly quotes Luke 4:23-27, including the specific verse Luke 4:24. This is a clear and direct allusion.
"And he said unto them, Ye will surely say unto me this proverb, Physician, heal thyself: whatsoever we have heard done in Capernaum, do also here in thy country. And he said, Verily I say unto you, No prophet is accepted in his own country. But I tell you of a truth, many widows were in Israel in the days of Elias, when the heaven was shut up three years and six months, when great famine was throughout all the land; But unto none of them was Elias sent, save unto Sarepta, a city of Sidon, unto a woman that was a widow. And many lepers were in Israel in the time of Eliseus the prophet; and none of them was cleansed, saving Naaman the Syrian."
Ellen White directly references Luke 4:23-27 in this passage.
"rejected the warnings of the Spirit through the Lord's messengers. Thus they cut themselves off from the channel by which God's blessing could come to them. The Lord passed by the homes of Israel, and found a refuge for His servant in a heathen land, with a woman who did not belong to the chosen people. But this woman was favored because she had followed the light she had received, and her heart was open to the greater light that God sent her through His prophet. DA 238.4"
"For this people’s heart is waxed gross, and their ears are dull of hearing, and their eyes they have closed; lest at any time they should see with their eyes, and hear with their ears, and should understand with their heart, and should be converted, and I should heal them."
Both passages deal with the rejection of God's message and the consequences thereof. Matthew 13:15 describes a people whose hearts are hardened and unwilling to receive the truth, while the EGW passage describes the Israelites rejecting the warnings of the Spirit and thus cutting themselves off from God's blessing. The parallel lies in the rejection and its consequences.