Can Christian dialogue with other religious traditions be a part of the calling to proclaim the gospel of the kingdom that Jesus preached?

Yes their are. Because dialogue is all about being at peace with each other, and Jesus taught us to love our neighbors as we love ourselves.

Jesus said in Mark 12: 31 According to NLT

"The second is equally important: 'Love your neighbor as yourself.’ No other commandment is greater than these". In this verse Jesus didn't tell us to love only fellow Christians, but he said your neighbors, knowing fully well that your neighbors could be fornicators, thieves, islamic, Jewish, Hindu, any many more, but he insisted you should love them, that means you should always be at peace with them.

This practically means that any Christian who is not in dialogue with people in other religions, such person is not a follower of Christ Jesus. The kingdom which Jesus preached is referred as a kingdom of peace, and you can only inherit that kingdom if you have proved yourself to be peaceful here on Earth.

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