Your understanding of Christianity and it's practicionsers seems some what limited. Perhaps more study in in order to understand the boundaries of what is Christians and what is cult would be in order. For example I do not know where you get the idea that Lutheran baptism is not accepted by Baptist. Perhaps a local Church made such a request of a new member but I also know Lutherans, as well as Catholics and others who have not been required to do so by the Baptist Church. Further more from personal experience I know the Methodist Baptism is accepted by the Greek Orthodox Church.
It is not your fault, proper Christian instruction in this liberal age is hard to come by regardless of the denomination, but there are boundaries that all Catholic, mainline Protestant and Orthodox agree with starting with the Trinity.
Southern Baptist Churches are autonomous and acceptance varies from church to church.
I was "sprinkled" by a Lutheran Chaplain and that was not acceptable with the Baptist Church I joined.
It is not your fault, proper Christian instruction in this liberal age is hard to come by regardless of the denomination,
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So very true and so very much a problem.