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Charcoal, 21 bytes

∧⁼§θ⁰§η⁰⁼↧⪫⪪θ_ω↧⪫⪪η_ω

Try it online!

This prints a - for truthy and nothing for falsey.

Link to the verbose version. It first compares the first character of both input strings (⁼§θ⁰§η⁰) and then compares the rest of both strings after removing the underscores (⪫⪪θ_ω) and converting to lowercase ().