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