Q. My mother was born Jewish but married a gentile and I was baptised and as a child was brought up as a Christian. I now want to be recognised as a Jew out of conviction. Do I need to re-convert?
A. Because of your maternal background you are Jewish according to Jewish law. But the matter is complicated by the fact that you were officially received into Christianity and practised it (though you do not tell me whether you have followed the Christian faith in the years since your childhood).
Therefore your acceptance of Judaism needs to be confirmed by means of immersion in a mikvah and a declaration of acceptance of the Torah.
In the first instance you should consult an orthodox rabbi and follow his advice. It is unlikely that any obstacles will be placed in your way.
In fact the return to Judaism which you seek is bringing an increasing number of people back to the Jewish fold.
If all or even most of the people in your situation re-asserted their Judaism, both they and we would be immensely strengthened.