Looks and income may change, but personality doesn't
Looks and income may change, but personality doesn't＝見た目や収入は変わるかもしれないが、性格は変わらない
見た目＝looks, appearance
収入＝income, salary
性格＝personality
may＝かも
この場合may changeなので「変わるかもしれない」と言う意味になります。
I think personality is the most important factor to consider when choosing a partner＝パートナーを選ぶ時に一番大事な事は性格だと思う
I think people's personality is the most important when it comes to finding the ideal partner because people's physical appearance and their income change, but their personalities never change.
この場合、次のような言い方ができますよ。
ーI think people's personality is the most important when it comes to finding the ideal partner because people's physical appearance and their income may change, but their personalities never change.
「理想のパートナーを見つけるのに関しては、人の性格が一番大切だと思う。なぜなら、外見や収入は変わることがあっても、性格は一生変わらないから」
physical appearance「外見」
personality「性格」
ご参考まで！
アメリカ合衆国 
カナダ 
