As is well understood, John's Gospel is not so much about the story of Jesus but the theology of Jesus; hence the ancient epithet, "John the Theologian" on hagiography.

John 10 refers to John 9 and the very significant miracle of restoring the sight of a man born blind (John 10:21). Further, the statement of John 10:30 about being one with the Father follows on the heels of John 10:1-16 about Jesus claiming to be the "Good Shepherd", another direct allusion to the claims of YHWH God in the OT: Ps 23, Eze 34:11-24 and Jer 31:9, 10 (more on this last reference shortly).

As if to reinforce this point, Jesus then makes the statement (v17, 18):

The reason the Father loves Me is that I lay down My life in order to take it up again. No one takes it from Me, but I lay it down of My own accord. I have authority to lay it down and authority to take it up again. This charge I have received from My Father.

This, in effect, repeats Jesus' claim in John 2:19, Jesus answered, “Destroy this temple, and in three days I will raise it up again.” Note His claim to raise Himself.

Shortly afterward at "the feast of dedication" (John 10:22), the same themes are taken up again about Jesus being the Good shepherd and being the sources of eternal life (v28). [This is a regular theme of John: "I am the bread of life" John 6:35-51; "I am the resurrection and the life", John 11:25; "I am the way the truth and the life", John 14:6, "I am the vine", John 15:1-5; see also 1 John 5:10-12.]

As part of this discussion with the Jews, Jesus then claims (v30):

I and the Father are one.

In the above context, the Jews understood Jesus explosive claims and immediately accused Him of blasphemy (v33), “We are not stoning You for any good work,” said the Jews, “but for blasphemy, because You, who are a man, declare Yourself to be God.”

Was Jesus alluding to the Shema in Deut 6:4? Yes and No. "Yes" because the idea is certainly superficially similar but there are important differences:

• Jesus changes the wording from "LORD" (YHWH) in the Shema to "Father"; However, in the NT this is understandable because Jer 31:9 combines the allusion of YHWH as both Shepherd and Father of Israel. The Jews were well aware of this because they understood their God, YHWH, as both "Shepherd" and "Father".
• the word for "one" is changed from εἷς (masc, LXX) to ἕν (neut). The effect of this is to affirm Jesus' unity of essence with the Father. See below.

Therefore, if Jesus is alluding to the Shema, He is probably combining those ideas with the constant and strident monotheism of the OT as well:

• Deut 4:35, You were shown these things so that you might know that the LORD is God; besides him there is no other.
• Deut 32:39, See now that I myself am he! There is no god besides me. I put to death and I bring to life, …
• Isa 44:6, Thus says the LORD, the King and Redeemer of Israel, the LORD of Hosts: “I am the first and I am the last, and there is no God but Me."
• Is 45:5, 6, I am the LORD, and there is no other; there is no God but Me … so that all may know, from where the sun rises to where it sets, that there is none but Me; I am the LORD, and there is no other.

[In the LXX, Deut 32:39 contains the unpredicated phrase, ἐγώ εἰμι (I am!). This title of YHWH is repeated in the LXX in other places such as Isa 41:4, 43:10, 13, 25, 45:19, 46:4, 48:12, 51:12, 52:6]

Thus, Jesus both affirms the theology of a single God and simultaneously claims His unity of being with the Father. No wonder Jesus was accused of blasphemy by claiming to be God (John 10:33).

CONCLUSION

I suggest that Jesus was alluding to the Shema but much more than the Shema.

APPENDIX - comments by others about the neuter form Jesus used in saying "I and the Father are one (neuter)".

Ellicott:

I and my Father are one.—The last clause of John 10:29 is identical with the last clause of John 10:28 if we identify “Father’s” with “My.” This our Lord now formally does. The last verses have told of power greater than all, and these words are an assertion that in the infinity of All-mighty Power the Son is one with the Father. They are more than this, for the Greek word for “one” is neuter, and the thought is not, therefore, of unity of person, but is of unity of essence. “The Son is of one substance with the Father.” In the plural “are” there is the assertion of distinctness as against Sabellianism, and in the “one” there is the assertion of co-ordination as against Arianism. At recurring periods in the history of exegesis men have tried to establish that these words do not imply more than unity of will between the Father and the Son. We have seen above that they assert both oneness of power and oneness of nature; but the best answer to all attempts to attach any meaning lower than that of the divinity of our Lord to these His words is found here, as in the parallel instance in John 8:58-59, in the conduct of the Jews themselves. To them the words conveyed but one meaning, and they sought to punish by stoning what seemed to them to be blasphemy. Their reason is here given in express words, “because that Thou, being a man, makest thyself God” (John 10:33).

Barnes:

I and my Father are one - The word translated "one" is not in the masculine, but in the neuter gender. It expresses union, but not the precise nature of the union. It may express any union, and the particular kind intended is to be inferred from the connection. In the previous verse he had said that he and his Father were united in the same object that is, in redeeming and preserving his people. It was this that gave occasion for this remark. Many interpreters have understood this as referring to union of design and of plan. The words may bear this construction. In this way they were understood by Erasmus, Calvin, Bucer, and others. Most of the Christian fathers understood them, however, as referring to the oneness or unity of nature between the Father and the Son; and that this was the design of Christ appears probable from the following considerations:

1. The question in debate was (not about his being united with the Father in plan and counsel, but in power. He affirmed that he was able to rescue and keep his people from all enemies, or that he had power superior to men and devils that is, that he had supreme power over all creation. He affirmed the same of his Father. In this, therefore, they were united. But this was an attribute only of God, and they thus understood him as claiming equality to God in regard to omnipotence.

2. The Jews understood him as affirming his equality with God, for they took up stones to punish him for blasphemy John 10:31, John 10:33, and they said to him that they understood him as affirming that he was God, John 10:33.

3. Jesus did not deny that it was his intention to be so understood. See the notes at John 10:34-37.

4. He immediately made another declaration implying the same thing, leaving the same impression, and which they attempted to punish in the same manner, John 10:37-39. If Jesus had not intended so to be understood, it cannot be easily reconciled with moral honesty that he did not distinctly disavow that such was his intention. The Jews were well acquainted with their own language. They understood him in this manner, and he left this impression on their minds.