Morality is subjective. You think attempting to convert people is immoral, while the people doing it think it’s very moral. You’re both right, or wrong. Objectively, it’s neither. It’s a free expression of ideas.
I note in the OP you have some perception of proselytizing as actually forcing someone to your point of view - which, again, objectively we’re in a grey area, but most major religions would seem to disagree with the idea of forced converts, even if some of their followers engage in such practices. Ethically, it’s deplorable, to try and forcibly change someone’s mind.
But that’s not proselytizing. That’s coercion.
From the perspective of the Christian Missionary, we’ll call him John Q. Baptist - he thinks that all non-Christians are going to burn in Hell for Eternity. Actually, more than that - he believes it as certainly as he believes in the ground under his feet. What does his belief instruct him to do, then? Well, he should make an effort to save these people from that fate. So John witnesses. He goes out into the world, trying to exemplify the Christian dogma, and bring the word of God with him. It’s the only choice he has, under his belief system, if he wants to be a Good person. For him to consider for a second that what he was doing was immoral, would require sudden, severe doubt on his part in his own belief system.