Halcon, but then the WTS does recognize the baptisms of other religions. Definitely 1956 and after, but most likely rebaptism was required after 1918, the WTS at time said that its members (all anointed because there was no great crowd identified then, all were anointed) were being taken to heaven in 1918. Is this confusing, and the has been forthcoming in explaining in their history. Only those baptized before 1918 did not have to be baptized again. While the exact details of Charles Taze Russell's personal baptismal practices before 1918 are not definitively documented, the organization later established that immersion before 1918, coupled with a shift away from a previous religious affiliation and affiliation with the Watch Tower, was considered valid.
But in 1956, is was stated definitely, people needed to be rebaptized by jws.
WT 1956 July 1 p. 406 pp.14 βOften the question is asked whether one baptized previously in a ceremony performed by some other religious group should again be baptized when coming to an accurate knowledge of the truth and making a dedication to Jehovah. Because of what has been already said, now there is compelling reason for also saying, Yes, one must be baptized again. Obviously, by any of such religious systems one was never in reality baptized βin the name of the Father and of the Son and of the holy spirit,β because had he been so baptized he would have appreciated the authority and office of such true Higher Powers. And if previously dedicated to Jehovah, the individual would have separated himself from such God-dishonoring Babylonish systems even before letting them baptize him. So the act of being baptized is not the important thing, but, rather, that which the act symbolizes is the element of importance.β
My grandparents were baptized as Bible Students (what members of the WTS were known back then (changed to Jehovah's witnesses in 1931 by Rutherford) and had been Lutherans and had to cut off all ties with their church.