I don’t like the idea of pushing away anybody sincere who wishes to join our people and accept Torah. The Torah commands us 36 times to love the ger, and I see the takanah as being at odds with that.
BUT, the takanah is halachically legitimate. It began in Buenos Aires by the Diber Shaul. It spread to America in 1935. Hacham Ouziel, zt”l, defended the legitimacy of the community’s right to enact the takanah, despite his own shitos on giyur.
The SY takkanah was passed because they felt they needed to put gedarim to protect them from assimilation.
The reason why historically, a ger was turned away three times was because of fear of persecutions. We were a proselytizing religion in Roman times, but that soon changed due to persecutions.