It certainly means to be seeking God and His Kingdom.
Those who have found or have been found by Jesus and are in the Kingdom have repented and have passed over the judgement because Jesus has taken their sins on Himself.
If Jesus took on the sins of the whole world, then that includes everyone regardless of their culture, history, or religion. So then, even if one remains a Buddhist their whole lives, if they live the law of love, which Jesus taught, then Jesus opening the doors to heaven, would pertain to them, and everyone else in the world regardless of actual religious affiliations. The Door, is Christ, not church affiliation, right?
God is calling us closer all the time, both in belief and practice.
Do you have scripture to support this statement that we are to get closer in "belief and practice"? My interpretation of scripture is that we are to draw closer to God with our
hearts, not with our religious beliefs and practices. We may choose to do that as a means to that end, if that is what we need for who we are and where we are at on our paths, but the injunction from Jesus is not to become more religious. Rather it's to become more loving, from what I read.
God does want us to repent and to accept Jesus, the one He sent, as our Lord and Saviour. Without Jesus sacrifice for us we face the judgement and can only hope for mercy, we cannot claim to be good enough and we cannot claim the sacrifice of Jesus for ourselves, we can only hope that God looks at our life and is merciful to us.
Are you saying that in order for Christ's sacrifice to be imparted to the whole world, somehow people must mentally acknowledge the doctrines of the Christian church and believe in them and follow them, i.e., convert to that religion? Are the keys to the kingdom, found in correct beliefs? Do we have to answer the questions on the test correctly first, demonstrating we have a correct mental comprehension of the Divine, in order to receive God's Grace?