In John 8:44, Jesus is not speaking to or of all Jews in general, but specifically to the Jews that had believed in Him (8:31; RSV, ESV). The Greek word used here is πεπιστευκότας (pipisteukotas), the perfect participle of the verb πιστεύω (pisteuō) - believe (or, equivalently, have faith in; there is no distinction in Greek).
Verse 31 is in contrast to verse 30:
So Jesus said, “When you have lifted up the Son of man, then you will know that I am he, and that I do nothing on my own authority but speak thus as the Father taught me. And he who sent me is with me; he has not left me alone, for I always do what is pleasing to him.” As he spoke thus, many believed in him (John 8:28-30).
One modern commentary explains here:
In the two verses 30 and 31, in which forms of pistevō, "believe," are found (the first, epistevsan, aorist, and the second, pepistevkotas, perfect participle), "believed" is the translation of both in the KJV.1 . There seems to be, however, a subtle difference between them. The first, being an aorist or past, has to do with the Jews initial reaction to the Lord's words. The second, being a perfect participle, might better be rendered as "had believed," hinting at a waver in their belief. This conclusion is supported by the dialogue in the verses that follow, 33-392
They answered him, “We are descendants of Abraham, and have never been in bondage to any one. How is it that you say, ‘You will be made free’?” Jesus answered them, “Truly, truly, I say to you, every one who commits sin is a slave to sin. The slave does not continue in the house for ever; the son continues for ever. So if the Son makes you free, you will be free indeed. I know that you are descendants of Abraham; yet you seek to kill me, because my word finds no place in you. I speak of what I have seen with my Father, and you do what you have heard from your father.” They answered him, “Abraham is our father.” Jesus said to them, “If you were Abraham’s children, you would do what Abraham did
This chastisement continues through verse 44.
So here the sequence was that there were some Jews that believed in him (v.30); Jesus, however knew that their hearts had turned to doubting and sought to bring them back (v. 31); those particular Jews took offense at Jesus' claim that He could make them free (v.32), not understanding that he was speaking spiritually and not carnally (v.33-36); and so forth. As the aforementioned commentary explains:
Those Jews who had some inclination to believe on the Lord because of His words, have now been offended at the intimation that they have need of being set free. In their mind, fleshly descent from Abraham guaranteed their freedom, at least of spirit, in spite of their physical enslavements of the past. What they have not understood is that their slavery was spiritual, because they had become servants of sin.3
Augustine comments here:
And now what answer did they give Him? For they began somewhat to realize that the Lord was not speaking of carnal generation, but of their manner of life. And because it is the custom of the Scriptures, which they read, to call it, in a spiritual sense, fornication, when the soul is, as it were, prostituted by subjection to many false gods, they made this reply: Then said they to Him, We be not born of fornication; we have one Father, even God. Abraham has now lost his importance. For they were repulsed as they ought to have been by the truth-speaking mouth; because such was Abraham, whose deeds they failed to imitate, and yet gloried
in his lineage. And they altered their reply, saying, I believe, with themselves, As often as we name Abraham, he goes on to say to us, Why do ye not imitate him in whose lineage ye glory? Such a man, so holy, just, and guileless, we cannot imitate. Let us call God our Father, and see what he will say to us.4
1. As he spake these words, many believed on him. Then said Jesus to those Jews which believed on him, If ye continue in my word, then are ye my disciples indeed.
2. Dmitry Royster, The Holy Gospel According to Saint John: A Pastoral Commentary (St. Vladimir's Seminary Press, 2015), p.233-34.
3. Ibid., p.235
4. Tractate XLII, Homilies on the Gospel of John