No, I say what Paul teaches, that God exercises that right by choosing whoever chooses to cooperate with His condition for forgiveness. Here is the context for Rom. 9:15 (the full study is posted in the thread about Resolving Problematic Interpretations):
29. In Romans 9:1-5 Paul notes how sad it is that those who are part of the human ancestry of Christ reject him as Messiah, but being a member of Abraham’s spiritual children is what is crucial (#17).
30. Romans 9:6-13 states that God had chosen which one of Rebecca’s sons (through whom Messiah’s lineage would be traced) before they were born (cf. Mal. 1:2-3). The word translated as “hate” (miseo) is the same as in Luke 14:26 with reference to family, so a better translation would be “preferred”: loving Jacob/hating Esau refers to God preferring that Jacob’s descendants serve as the heritage for Messiah rather than to individual salvation.
31. Romans 9:14-16 stresses that s/e depends on God’s mercy rather than being achieved by human effort (#12), although the preceding context has shown that (the non-meritorious condition of) faith is involved, which truth can be stated as “God initiates; sinners cooperate—or not”, because of MFW.
32. Romans 9:17 refers to pharaoh in Exodus 9:13-35 as an example of someone whom God allowed to oppose His will so that His power might be manifested by the plagues. The OT passage indicates that pharaoh was conscious of his sin but “He and his officials hardened their hearts” (v.34b).
33. Romans 9:18 says that God “hardens whom He wants to harden”, which raises the question asked in v.19, “Why does God blame sinners who cannot resist His will?” Paul’s response (Rom. 9:20-21) is that God has the might and thus the right to determine what is right. Then he speculates (“What if”) that God might have patiently endured evildoers (#20) as evidence of His glory toward recipients of His mercy (Rom. 9:22-23).
34. In Romans 9:24-33 and 10:1-4 Paul notes that God elected to choose Gentiles with saving faith instead of Israelites who sought salvation by works and stumbled over the Gospel of Christ, even though “everyone who believes” receives righteousness or s/e.
35. Romans 10:9 states God’s requirement for s/e as “confess Jesus as the resurrected Lord”, v.10 clarifies that the condition of faith (#31) precedes the work of confession, and vs.11-13 reiterate that all sinners who call on the name of the Lord will be s/e.
36. Romans 10:18 cites Psalm 19:4, which hints that God’s s/e has been possible for everyone in the world. This implication may also be seen in Gal. 3:8, Col. 1:23 and Tit. 2:11 as well as Rom. 1:20.
The concerns of those who accept TULIP—to affirm the sovereignty of God and the inability of souls to earn salvation—are valid, but the solutions are problematic, because they deny or ignore Scripture teaching the love of God for all sinners and the moral accountability of sinners for rejecting the love of God, thereby effectively perverting the Gospel (Gal. 5:6) and impugning God’s justness/righteousness (Psa. 33:5, Isa. 9:7).
The apparent reasons for these errors are threefold:
1. Ignorance of Scripture that contradicts their dogma, such as those teaching the possibility of apostasy,
2. Viewing faith as a meritorious work rather than as the non-meritorious condition of cooperating with God’s grace, and
3. Unconcern about portraying God as unjust by showing favoritism toward the elect. Once these errors are cured by including Scripture supporting MFW, doctrinal harmony is enhanced.
Hope this helps,