It's less that they're becoming similar and more that they're 'birds of a feather,' you know.

Literal

Resemble-[come-てくる][quotative-と] say-[rather-than-よりは] like-attracts-like [like-みたいな] feel is-[polite-です][confirmation-ね].

Casual observation. 類友 is a colloquial contraction of the proverb 類は友を呼ぶ ('like attracts like,' literally 'the kind calls its friends') — the equivalent of English 'birds of a feather flock together.' ~と言うよりは 'rather than saying X' is a common contrastive construction for choosing between two characterizations. 似てくる uses ~てくる for a gradual coming-into-resemblance over time.