Is Jesus' statement that Satan is the father of the Jews anti-Jewish?

Jesus was himself a Jew therefore I am perplexed by your question. Jesus was not a racist, what that passage is intended to convey is that:

Genesis 15:4through 6 NKJV And behold, the word of the LORD came to him, saying, "This one shall not be your heir, but one who will come from your own body shall be your heir." 5 Then He brought him outside and said, "Look now toward heaven, and count the stars if you are able to number them." And He said to him, "So shall your descendants be." 6 And he believed in the LORD, and He accounted it to him for righteousness.

and even though they were speaking with one who spoke with the authority of God they still did not believe, and were therefore unrighteous.

The key to understanding this passage lies in:

John 8:37 through 40 NKJV "I know that you are Abraham's descendants, but you seek to kill Me, because My word has no place in you. 38 I speak what I have seen with My Father, and you do what you have seen with your father." 39 They answered and said to Him, "Abraham is our father." Jesus said to them, "If you were Abraham's children, you would do the works of Abraham. 40 But now you seek to kill Me, a Man who has told you the truth which I heard from God. Abraham did not do this.

The 'Old Timers' of my youth used to quote these Scriptures when they used the term "Like father like son".

No, God is no respecter of persons (Acts 10:34)

"But, in every nation whoever fears Him and works righteousness is accepted by Him." (Acts 10:35)

Jesus was not speaking about Jews as a nation, but specifically to the audience in-front of Him. They have hardened their hearts against the Holy Spirit and were working against God.

Jesus was talking to a subset of people who were Jewish. Abraham was, in fact, their father/ancestor. However, being Jewish was not merely physical. They were God's covenant people. In this covenant, God obligated Himself to various things, but they were also obligated to various things as well. Also, a Jew who did not worship God and God alone was to be cut off from his people.

The Jews Jesus was speaking to in this particular passage were not worshiping God and God alone. In fact, Jesus, the Eternal Son, was standing before them, and they rejected Him. There is not much more they could do to completely reject God.

However, there were other Jews to whom He gave incredible praise. John the Baptist was one of them. In fact, when Jesus taught His disciples to pray, He instructed them to address God as "Father".

So, the Jews who rejected Jesus had rejected God's covenant with Abraham and, though, they were physically of Abraham, God was no longer their God or Father. Yet, to the Jews who believed in Him, He affirmed that God was their father.

Is there some way of understanding this verse to be not anti-Jewish, or are there Christians that do not accept this verse as authoritative?

The particular Jews that Jesus was speaking to were plotting to kill him. Jesus was pointing out that their claim to Abraham may have had a biological basis, but that their actions were contrary to what Abraham would have done. Jesus was in essence telling them that they have no legitimate claim to Abraham since their actions denied him.

John 8:37-39 I know that ye are Abraham's seed; but ye seek to kill me, because my word hath no place in you. I speak that which I have seen with my Father: and ye do that which ye have seen with your father. They answered and said unto him, Abraham is our father. Jesus saith unto them, If ye were Abraham's children, ye would do the works of Abraham.

This particular group of Jews then raised the stakes. Jesus implies that their "father" is not Abraham but someone else. They then turn this insult back on Jesus (maybe implying illegitimacy regarding his birth). They then declare God as their father.

John 8:40-41 But now ye seek to kill me, a man that hath told you the truth, which I have heard of God: this did not Abraham. Ye do the deeds of your father. Then said they to him, We be not born of fornication; we have one Father, even God.

Jesus completes his explanation of why this group of Jews is unable to accept him. It is because they are in alignment with one who is hostile to God. They have come to a point where their connection to Abraham and God is of none effect.

John 8:42-44 Jesus said unto them, If God were your Father, ye would love me: for I proceeded forth and came from God; neither came I of myself, but he sent me. Why do ye not understand my speech? even because ye cannot hear my word. Ye are of your father the devil, and the lusts of your father ye will do. He was a murderer from the beginning, and abode not in the truth, because there is no truth in him. When he speaketh a lie, he speaketh of his own: for he is a liar, and the father of it.

What a powerful warning this is for us. This particular group of Jews had come to a point where everything they did was contrary to what a Jew was supposed to do. They had in effect made themselves non-Jews by accepting a different "father".

Jesus is not calling all Jews "of the devil". He is telling those Jews who are trying to figure out a way to kill him that their opposition to him is because they have adopted a different "father".

That is exactly not the point he is trying to make. He is trying to say that it's our actions that show whether God or Satan is "our father" in a very figurative sense. He is saying "You are not the righteous just because you descend of Abraham, if you not also behave like that". Reversing that to say Jews are "children of Satan" in general is basically the thing he tries to refute here, in reverse.