You seem to have the wrong idea about Calvinist beliefs. Yes, they do believe what the bible says about God having chosen people before the foundation of the world. They also believe that all who believe on the Lord Jesus Christ will be saved. Why do some believe and others not? Not because the believers are cleverer, more spiritual. No, because God has given them new life:
“And you [He made alive], who were dead in trespasses and sins, in which you once walked according to the course of this world, according to the prince of the power of the air, the spirit who now works in the sons of disobedience, among whom also we all once conducted ourselves in the lusts of our flesh, fulfilling the desires of the flesh and of the mind, and were by nature children of wrath, just as the others. But God, who is rich in mercy, because of His great love with which He loved us, even when we were dead in trespasses, made us alive together with Christ (by grace you have been saved), and raised [us] up together, and made [us] sit together in the heavenly [places] in Christ Jesus, that in the ages to come He might show the exceeding riches of His grace in [His] kindness toward us in Christ Jesus. For by grace you have been saved through faith, and that not of yourselves; [it is] the gift of God,” (Eph 2:1-8 NKJV)
Strange how when I refer to C/R views as being a problem I get the same type of answer "You seem to have the wrong idea about Calvinist beliefs.". I quote calvinists and am still told that is not what C/R's believe. Really then why do they say they do.
Just as you did in this post. You said there were a select group of "chosen people before the foundation of the world." then that logically requires that there be all those that were not chosen.
And you say that even though the bible tells us that it is God "who desires all men to be saved and to come to the knowledge of the truth" and He sent Christ "that the world might be saved through Him" And we know God meant all of humanity unless you think only that select group were "ungodly, sinners".
The bible is clear that Christ was not just "the propitiation for our sins" but "the whole world" because He "gave Himself as a ransom for all"
And we can know this truth by "the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek."
So that "In Him, you also, after listening to the message of truth, the gospel of your salvation—having also believed, you were sealed in Him with the Holy Spirit of promise, who is given as a pledge of our inheritance, with a view to the redemption of God's own possession, to the praise of His glory."
So either the word of God is wrong or your understanding of Eph 1:4 is. I will go with the bible. No one was chosen “
to be” in Him but instead that those who have repented and believed and are now “in Him” through faith are promised and predestined to an inheritance, adoption, and to be holy and without blame.
FYI Eph 2:1-10 is true. We were lost in our sin but when we freely trusted in His son were were made alive in Him. Only God can save and He has chosen to save those that trust in Him "For by grace you have been saved through faith; and that not of yourselves, it is the gift of God;"
So while the C/R view is that only a select group were picked out the bible tells us "WHOEVER WILL CALL ON THE NAME OF THE LORD WILL BE SAVED." and John adds these words "these have been written so that you may believe that Jesus is the Christ, the Son of God; and that believing you may have life in His name."
Christ does not give them life so they will believe He gives life to those that believe to those that are in Christ through faith. "Even so consider yourselves to be dead to sin, but alive to God in Christ Jesus." "if we have died with Christ, we believe that we shall also live with Him" And we are told to "present yourselves to God as those alive from the dead, and your members as instruments of righteousness to God." "For sin shall not be master over you, for you are not under law but under grace."
" But thanks be to God that though you were slaves of sin, you became obedient from the heart to that form of teaching to which you were committed, and having been freed from sin, you became slaves of righteousness."