This is a question about who will be saved. John 5:22 says God has given all judgment to the Son. Therefore we should be cautious not to pre-empt the judgment of Christ or attempt to usurp his authority by making judgments on his behalf. The most we can do is examine the scriptures for the statements they make about who will be saved.
Regarding the relevance of “thorough theological knowledge” for salvation, it is an interesting study to examine all the passages in the scriptures that talk about the judgment seat. For myself I have not found a single passage that stipulates knowledge as a criteria for salvation or where someone is rejected for insufficient knowledge. To take just one example, the Parable of the Sheep and the Goats, in this context the judgment based upon actions (e.g. “for I was hungry and you gave me no food …” Matt 25:42), there is no mention of knowledge. In this sense it does not seem that knowledge, in-and-of-itself, is relevant to the judgment.
This being said there are some passages that stipulate faith requirements for salvation, most frequently belief in Jesus:
For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life (John 3:16)
Whoever believes in him is not condemned, but whoever does not believe is condemned already, because he has not believed in the name of the only Son of God (John 3:18)
Whoever believes in the Son has eternal life; whoever does not obey the Son shall not see life, but the wrath of God remains on him (John 3:36)
For this is the will of my Father, that everyone who looks on the Son and believes in him should have eternal life, and I will raise him up on the last day (John 6:40)
These are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name (John 20:31)
This faith is probably not beliefs about Jesus (e.g. “Jesus was a man”, “Jesus was born in Bethlehem”, etc.) but more likely trust in Jesus (e.g. “Jesus is able to save me”). This is different from “theological knowledge”; some people might class it as knowledge as it involves mental content. However you want to term it, it seems to involve a conscious confession of Jesus and his power to save you from your sins.
Now if a conscious confession of Jesus is a requirement for salvation then that might seem to exclude those unable to make such a confession, i.e. those unable to understand the confession that they are making. Those, like Christadelphians, who only practice adult baptism do so because they believe baptism is meaningless unless the one being baptised is able to understand what it means. If this conclusion is correct then it might exclude the severely disabled and the very young from salvation if they are unable to make such a confession.
Having said all this, Jesus says of children:
“See that you do not despise one of these little ones. For I tell you that in heaven their angels always see the face of my Father who is in heaven … it is not the will of my Father who is in heaven that one of these little ones should perish” (Matt 18:10-14)
It is statements like these that should warn us against making our own judgments about the decisions God has put under the authority of the Son. Instead we who know his will should do it (i.e. believe in the Son and be baptised in his name) and trust in the grace of him to whom these judgments have been entrusted.