In context, who is being addressed? Israel. (vs. 1) What was the problem? Romans 10:3 - For they being ignorant of God’s righteousness, and seeking to establish their own righteousness, have not submitted to the righteousness of God. For Christ is the end of the law for righteousness to everyone who believes. Seeking justification by law = zeal for God but not according to knowledge here. So, accusing me of having a zeal for God but not according to knowledge by citing Romans 10:2 is a false accusation. I am not an Israelite who is seeking justification by law. My faith is in Jesus Christ for salvation and is not in my own righteousness which is from the law. (Philippians 3:9)
John 6:40 - For my Father’s will is that everyone who looks to the Son and believes in him shall have eternal life, and I will raise them up at the last day. So, in John 6:40 and Romans 10:4 we see that those who believe have submitted to the righteousness of God and shall have eternal life. Elsewhere in Scripture, Jesus repeated multiple times that those who believe shall have eternal life. (John 3:15,16,18; 5:24; 6:29,40,47; 11:25,26) The apostle Paul also repeatedly said in Scripture that those who believe will be saved. (Acts 13:39; 16:31; Romans 1:16; 4:5-6; 1 Corinthians 1:21)
Should we also accuse Jesus and Paul of cherry picking and disregard those verses or should we believe Jesus and Paul?