Following up on my Baptist Chronicles post, here's a quote from David Docery in Calvinims: A Southern Baptist Dialogue:
We must recognize that there is a need for boundaries to say that some things do not fit in Baptist life. We need to say that hyper-Calvinims (involving the rejection or neglect of evangelism and missions) does not fit. We need to say that consistent Arminianism (involving the rejection of eternal security) does not fit. Pelagianism, open theism and process theology do not belong. (p. 42)
Docery does not like the label Arminianism because of its association with the rejection of eternal security providing another example of why non-Calvinist Southern Baptists don't call themselves Arminian.