I am responding – against my better judgement – because I think this is too important an issue, at the moment more than ever, to ignore, and this is a public, searchable, forum.
You can, however, convert to Judaism and follow the religion but you are not Jewish
To quote your original comment on this “you are a Jew rather than Jewish”. I could almost understand your position if you had said “you are a follower of Judaism” (though would probably still have disputed it) but to make a distinction between being “Jewish” and “a Jew” makes no sense. As I said earlier, they have exactly the same root.
In rejecting the right of a convert to describe themselves as Jewish you are essentially othering them, which goes against the ethos (to my knowledge) of all the mainstream religious authorities in this area. When a convert to Judaism joins the chain of people that leads back to Sinai, they are regarded as indistinguishable from those who are Jewish by descent, inheriting that history and culture and becoming themselves part of it.
There's a whole other argument in fact - not one I intend to have in detail here - about Jewish "ethnicity"; consider the Jewish communities of Ethiopia, China, India... Jews are a people not a single genetic group. Whilst there are genetic traits associated with particular groups (Tay Sachs in the Ashkenazi community, for example) genetic studies have found that there is not a "Jewish gene".
We are agreed I think that converting to Judaism does not change someone’s ethnicity. Your argument seems to be that the word “Jewish” can only be applied to people with ethnically semitic ancestry (pace the above, and even though, as I said before, converts have always been part of that ancestral chain, from Ruth onwards). I fundamentally disagree with this; Jewish identity is simultaneously cultural, ethnic and religious, and can be a combination of any of these or just one. Someone can identify strongly as a Jew and never set foot in a synagogue, or be a strictly observant member of their religious community yet not have Jewish ancestry. Both archetypes are “Jewish”, in different ways. To aver otherwise is invidious. These are not binary positions.
I think we both know where this argument leads. Again I ask that we can agree to disagree on this, and leave it there.