Do Christians feel it's impossible to be Jewish and to also believe Jesus is the messiah?

I've had some very interesting e-mails and conversations with both Jews and Christians today based on how I answered a question about Jesus. I have been told by other Jews that I shame Judaism and was told by a Christian woman it's not possible to be Jewish and believe in Jesus. Didn't Jesus say, ask me to come into your heart and I will reveal myself to you? Wasn't Jesus Jewish? Weren't the first Christians Jewish? I am Jewish and found Jesus, yet feel as Jewish as I ever have. My Jewish cousin is a born again Christian, considers herself and her children Jewish, yet is Evangelical. Why are a handful of people so disturbed by this? The Christians I know welcome me with open arms and understand their Christianity and its connection to Judaism. I've spoken with Priests and Preachers of all religions and have researched this for 35 years. No one has told me I am shaming my religion, or has told me I can't be Jewish if I believe in Jesus. I take none of it personally and knows God loves all his children. Why don't they, or you, if you too feel that way?