Does John 10 teach that no one is shut out from God's plan of salvation?
Yes. John 10 presents Jesus as the door of the sheepfold, and He declares that any man who enters by Him shall be saved. The passage applies to God's plan of salvation, showing no one is shut out, though entrance is only through Christ, not by another way.
Les explains that John 10 is the great good shepherd chapter, where Jesus speaks during His earthly ministry and makes a perfect application that no one has been shut out from God's great plan of salvation. Les points out that Jesus uses the sheepfold and sheep. In verse 1, Jesus says the one who does not enter by the door but climbs up some other way is a thief and a robber, meaning you cannot just pick and choose; there is only one way. In verse 2, the one who enters by the door is the shepherd of the sheep; the porter opens to him, the sheep hear his voice, he calls his own sheep by name and leads them out. In verse 5, a stranger they will not follow but will flee from him, for they do not know the voice of strangers. In verse 9, Jesus says, “I am the door: by me if any man enter in, he shall be saved.” Les asks where the door to the sheepfold is, using the image of a place of safety for the sheep at night, which they called the fold. So the teaching is that salvation is open to any who enter by Christ, the one door, and no one is excluded from God's plan if they come His way.
Verily, verily, I say unto you, He that entereth not by the door into the sheepfold, but climbeth up some other way, the same is a thief and a robber.
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