I agree with you OP and I follow a Christian religion. I think it would be possible to introduce Christianity to non-Christian people by example of love and service to them, and to hope they might follow and ask more. At that point the Christian could offer to explain, but that is all.
Coming to God through Jesus, means through the teachings he gave -that in my opinion is what ‘though me’.
As to the post about the Muslim lady I agree it would have been wrong to push her. My church organises joint meetings of mutual respect with Muslims but not to persuade them to convert ( Muslims recognise Mary ans tge mother of Jesus, and also Jesus as a great prophet). God is God. Muslims (as opposed to Islamist extremists) already follow ideas which Jesus spoke about all be it through a different approach.
Luke said
KJ21
^Neither shall they say, ‘Lo, it is here!’ or ‘Lo, it is there!’ For behold, the Kingdom of God is within you.”
An egregious example of missionaries being harmful, aside from introducing viruses which decimated tribes, is of a missionary group who worked with a tribe of happy, peaceful innocent people, living their own way in spite of the 20th Century - the Panare Indians.
The missionaries told them about Jesus then needed to get them to repent for their sins for which Jesus has died for them, so they ‘translated’ the Bible into their language. Leaving out Judas, the Chief Priests and their followers, and Pontius Pilot who were responsible for the Crucifixion, they had it say that the Panares ancestors had made Jesus be crucified and God said they would burn in the fires of hell unless they became Christian and repented. They became riddled with guilt and terrified. Of course they became ‘Christian’s’.
For me those Panare people were the children of God, the missionaries certainly were not.
(It is easy to look accounts of this up.)
This example is extreme but missionaries should be extremely careful.