The word 'proselyte' is easily passed over as an old religious term. In the first-century Jewish world it could refer to a Gentile convert who had joined the Jewish people and accepted Jewish religious obligations.
Jesus uses the strenuous image of crossing sea and land not to condemn conversion itself, but to expose religious zeal that reproduces corrupt leadership.
Jewish communities existed throughout the Mediterranean world, and non-Jews could be attracted to Jewish monotheism, Scripture, ethics, and worship. Degrees of association varied, while full conversion for males came to include circumcision along with acceptance of Jewish communal obligations.
Evidence does not require us to imagine one centrally organized missionary program operating everywhere. Jesus' language emphasizes energetic effort: teachers may be intensely zealous to gain a convert while failing in the weightier matters of faithfulness.
The context makes the rebuke more precise. Zeal, travel, and success in winning adherents are not treated as proof that the resulting discipleship is sound.
Jesus measures religious leadership by truth and character, not merely by expansion. A convert shaped by corrupt teaching can reproduce and even intensify the faults of the teacher.