The sentence in question roughly means:
Ignoring it (="the fact that I have an ego and real feelings"), [someone] tries to (come to me and) treasure me (or take care of me).
大切にする is a set phrase meaning "to treasure" or "to take good care". Here, (-て)くる is a subsidiary verb that describes someone/something coming to the speaker, either physically or psychologically. Since the speaker (僕) is saying してくる instead of してくれる, we can tell he is somehow annoyed by how he is treated.
The characters in this picture (Ernst and 2B) use first-person pronouns other than 僕, so the text is about someone else who uses 僕. I think this text is written from the standpoint of 9S, another android protagonist of the game who calls himself 僕. He was at this scene, too. The subject of 無視する and 大切にする is not specified in the text, but it's probably 2B, if I remember their relationship correctly. All in all, the implication of the whole sentence is something like "She ignores my love, and treats me like an object/kid to be protected rather than a partner of equal status".