The album was co-produced by Jimmy Hogarth, and features contributions from Leo Abrahams, Chris Vatalaro, Samuel Dixon, and Rob Moose.

[3] Later, Hogarth brought together a studio band including Leo Abrahams, Chris Vatalaro, Samuel Dixon, and Rob Moose who provided string arrangements.

[3] The album covers a variety of topics, including prejudice within the context of a broader societal upheaval on "It Must Change" and environmentalism on "There Wasn't Enough".

[10] NME's Patrick Clarke wrote that Anohni "eschews experimental sonics for warm vintage soul, but the results are no less vital" on the album, which he felt is "the most accessible thing she's ever made".

"[18] Michael Cragg of The Observer noted that "Anohni continues to soundtrack oppression, loss and alienation with heart-aching precision" and that the arrangements "add a soulful swagger to often brutally direct lyrics".

"[20] Charles Lyons-Burt of Slant Magazine found that the album includes "some of Anohni's most laidback and unfussy arrangements to date" and "marked by minimalist, sometimes gloomy guitar strumming" but called it a "pity, then, that so much of the music on My Back Was a Bridge for You to Cross undeserves her anguished storytelling".

"[21] Joe Muggs of The Arts Desk concluded that the album "does feel like an artist continuing to inhabit themselves in a very thought-through way", which makes its sound "genuinely a bold choice, in the same way the electronics of its predecessor were.

[11] Richie Assaly of the Toronto Star states "the album sees the artist — whose celestial, sonorous voice remains a singular force of nature — resume her role as a radical truth-teller.

"[22] John Amen of Beats Per Minute wrote that the album, "shows Anohni pivoting between stunningly direct and entrancingly oblique manifestos.