If I were to say that I embraced Buddhism or some other mystical eastern religion as many of my brethren have, it would be considered hip or amusing or a sign I was interested in spiritual things but, to say I follow the risen messiah and all of a sudden I'm not even a Jew any more. That's more hurtful then being called a derogatory name by a gentile.
But, they don't realize that as human beings, they have no autority to say who God did or did not make a Jew.
The reason they get so angry is because deep down, they really do suspect that it's all true. And it scares them a little and with fear comes anger and resentment.
Oh, booh, hoo, hoo! If people are annoyed with you it is because you have rejected MONOTHEISM and chosen to throw your lot in with people who have persecuted us for 2,000 years. Get a grip - G-d does not like it when you disobey His Laws. By the way: why do people like you have a fratricidal jealousy of Judaism? is it because our presence reminds you that YOU ARE WRONG?????