Yes, they do have free will. In Romans 9-11 Paul is not teaching determinism; he is countering the deterministic views of his opponents.
Paul's Titanic Chiasmus
Romans 9-11 is a massive, chiastic argument, centered around the topic raised in Romans 9:3-5, and debated among the Roman Christians of the time:
- Are those physically born into Israel pre-determined to be heirs of God's covenants?
- Is everyone else ineligible?
Paul's response is a resounding "no!", but he develops this argument over 3 chapters, not 3 verses.
The center (most important part) of this chiasmus is in chapter 10:
12 For there is no difference between the Jew and the Greek: for
the same Lord over all is rich unto all that call upon him.
13 For whosoever shall call upon the name of the Lord shall be
Note that the emphasis in verse 13 is on the whosoever, not the call. The point is not to outline a checklist entitled "steps to salvation", but to clearly establish that God's covenant of grace--which Paul has spent much of this epistle outlining--is available to everyone.
Allegory of the Olive Tree
The critical verses highlighted in the OP are chiastically paired with the allegory of the olive tree in Romans 11. I review the development of Paul's argument in more detail in this post. I'll offer a more concise summary here.
I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.” 16 So then it depends not on human will or exertion, but on God, who has mercy.
The first sentence is a quotation of Exodus 33, which shows that God's decision to extend mercy (or judgement) is not arbitrary. The latter sentence builds on Paul's arguments from Moses & Jacob in the previous verses: you can't earn God's mercy. Moses & Jacob didn't earn God's mercy. But God, who knows people from the beginning (see Jer. 1:5) and knows the heart (see 1 Sam. 16:7), gave them what they could never earn, and in so doing created a covenant with them.
Paul spent the last few chapters explaining that salvation came through Christ, not through strict, unwavering obedience to the Law of Moses. Paul teaches that God's people are not under the Law of Moses; they are under grace.
Grace, in Paul's world, did not mean a handout. Grace was a gift that was given through covenant or treaty: there were expectations of the recipient (see further discussion in my videos here & here). Moses & Jacob were recipients of God's covenants. God's covenants were extended to ancient Israel (though not all chose to accept/keep these covenants). Paul's glorious message is that even though you too cannot earn it, you cannot attain it through human will & exertion, God extends His covenants to you as well! A portion of Paul's audience thinks they are better than their peers--he's telling them they are not.
Paul illustrates this reality in chapter 11, through the allegory of the olive tree (natural branches = physical Israel, wild branches = those adopted in). Those of physical Israel who are unbelieving are cut off from the olive tree, and no longer receive the "richness" of its roots (see vss. 17,20). Those who, though not of physical Israel, endure/persist/continue (ἐπιμένῃς, v22) and stand by faith (v20) are grafted into the tree and receive the richness of its roots.
Paul quickly warns, however, that those who were grafted in can still be cut off if they are prideful (v20), and those who have been cut off can still be rescued and returned to the tree if they turn from their unbelief (v23).
This is a decidedly non-deterministic theology. Paul does not dispute the Israelite claim to have been foreordained by God to be born into Israel--but he shows them, from their own prophets, history, and parables--that being born into Israel is not enough. One can gain access to God's covenants through faithfulness, and one can lose access through unfaithfulness. Although the Israelites received these opportunities first, they did not receive them exclusively: everyone, regardless of their family "tree" of origin, can be grafted in to be full heirs (see Romans 8:14-17).
Vessels of Wrath
The critical verb here, κατηρτισμένα (having been completely fitted, prepared), is not in active voice. God, the subject of the sentence, is not doing the action. Here Paul explains the clay analogy from the prior verse: God gives life to & sustains His creations--even the wicked ones--and permits them to pursue their chosen course.
The unfaithful prepare themselves for destruction. By not immediately squashing the clay and starting over, God is in fact merciful: He endures, He puts up with them, He grants them a time and a space to repent. It is when they are completely fitted/prepared for destruction--by their own agency--that God metes out destruction. This too is demonstrated on the opposite side of the chiasmus--even the branches that have been cut off can be restored if they turn from their unfaithfulness. God will show His power, mete out justice, and use it as a teaching moment for future generations, but He reserves destruction until people are "fully ripe" in iniquity.
The vessels of wrath do have free will, and they are using it poorly--fitting themselves to receive justice from God.
When Paul's argument is considered in its entirety, rather than severed into isolated pieces, it is clear that Paul is responding to determinism, not teaching it. Those who are willing to be led by the Spirit and remain faithful may receive all of the promises of Abraham, regardless of their physical lineage.