Calvinists, have no problem with this passage at all. Dead sinners always resist the Spirit of God. But when Spirit comes to regenerate, for the purpose of salvation, the dead sinner is made alive and willing, with no resistance.
Rather, there is a bigger problem for those Arminians who say that sinners are not really dead in sin or unable to come to God, how do they cooperate or respond to the Spirit if they always resist Him? There is said here much more than some Arminians would want to admit. The total depravity of human kind which without sovereign grace always resists the work of God.
This is what the ESV Study Bible says:[2]
Acts 7:51 Stephen concluded with a direct attack on Israel for rejecting the Messiah. While this may seem harsh, Luke will soon say that Stephen was “full of the Holy Spirit” (v. 55; cf. 6:10, 15) and he was no doubt led by the Spirit, who knew the hearts of Stephen’s listeners, to make this accusation. Using the language of the OT he accused them of being stiff-necked (see Ex. 33:3, 5; 34:9; Deut. 9:6, 13), uncircumcised in heart and ears (Lev. 26:41; Deut. 10:16; Jer. 4:4, 6:10, 9:26; Ezek. 44:7, 9), and resisting the Holy Spirit (Isa. 63:10). In fact, the repeated rejection of God’s will is the point of his story, justifying the charge that prophets also made against the nation.
John Gill comments on this:[3]
Ye stiffnecked,.... Or "hard necked", the same with קשה עורף, which is a character frequently given of this people, Ex 32:9 and elsewhere, and is expressive of their obstinacy, stubbornness and refractoriness; who would not submit their necks to the yoke of God's law, and be obedient to his commands:
and uncircumcised in heart and ears; for though they had the mark of circumcision in their flesh, of which they boasted; yet they had not the true circumcision of the heart; their hearts were not circumcised to fear and love the Lord, nor their ears to hear the word of the Lord and the Gospel of Christ; so that notwithstanding their confidence in carnal privileges, they were uncircumcised persons:
ye do always resist the Holy Ghost; the resistance made by these persons was not to the Spirit of God in them, of which they were destitute, but to the Spirit of God in his ministers, in his apostles, and particularly in Stephen; nor to any internal operation of his grace, but to the external ministry of the word, and to all that objective light, knowledge, evidence, and conviction that it gave of Jesus's being the Messiah: and such who resist Christ's ministers, resist him, and such who resist him, may be said to resist his Holy Spirit; and the word here used signifies a rushing against, and falling upon, in a rude and hostile way, and fitly expresses their ill treatment of Christ and his ministers, by falling upon them and putting them to death: which is the resistance here designed, as appears by the following verse: so that this passage is no proof of the resistance of the Holy Spirit, and the operations of his grace in conversion, when he is in men, and acts with a purpose and will to convert them; since it does not appear that he was in these persons, and was acting in them, with a design to convert them; and if he was, it wilt be difficult to prove that they so resisted, and continued to resist, as that they were not hereafter converted; since it is certain that one of them, Saul, was really and truly converted, and how many more we know not. Though it will be allo...