Non-binary prayers indicate that G-d is neither male nor female but a gender-free sovereign. "Depersonified" means that God is not anything resembling human concepts but is rather breath or spirit, also without gender.

בְּרוּךֶ אָתֶה ײַ, אֱלֹתְהֵינוּ מַלְךֶ הָעוֹלָם, שֶׁהֶחֱיָנוּ וְקִיְּמָנוּ וְהִגִּיעָנוּ לַזְמַן הַזֶּה
B’rucheh Ateh Yah, Elot’heinu mal’cheh ha’olam, she’he’cheh’yanu, v’ki’ye’manu, v’hi’gi’anu la’zman ha’zeh.
Blessed are You, G-d, our G-d, Sovereign of the Universe, who has kept us alive, sustained us, and brought us to this very moment.

De-personified:
בְּרוּךֶ אָתֶה ײַ, אֱלֹתְהֵינוּ רוּחַ​ הָעוֹלָם, שֶׁהֶחֱיָנוּ וְקִיְּמָנוּ וְהִגִּיעָנוּ לַזְמַן הַזֶּה
B’rucheh Ateh Yah, Elot’heinu ruach ha’olam, she’he’cheh’yanu, v’ki’ye’manu, v’hi’gi’anu la’zman ha’zeh.
Blessed are You, G-d, our G-d, Breath of the Universe, who has kept us alive, sustained us, and brought us to this very moment.

בְּרוּךֶ אָתֶה ײַ, אֱלֹתְהֵינוּ מַלְךֶ הָעוֹלָם, אֲשֶׁר קִדַשְׁתַנוּ בְּמִצְוֹתֶיהֶ וְצִוְתָנוּ עַל נְטִילַת לוּלָב
B’rucheh Ateh Yah, Elot’heinu mal’cheh ha’olam, asher kidash’tanu be’mitzvoteh’eh ve’tziv’tanu al ne’tilat lulav.
Blessed are You, G-d, our G-d, Sovereign of the Universe, who has sanctified us with G-d’s commandments and has commanded us on moving* the lulav.

De-personified:
בְּרוּךֶ אָתֶה ײַ, אֱלֹתְהֵינוּ ​רוּחַ​ הָעוֹלָם, אֲשֶׁר קִדַשְׁתַנוּ בְּמִצְוֹתֶיהֶ וְצִוְתָנוּ עַל נְטִילַת לוּלָב
B’rucheh Ateh Yah, Elot’heinu ruach ha’olam, asher kidash’tanu be’mitzvoteh’eh ve’tziv’tanu al ne’tilat lulav.
Blessed are You, G-d, our G-d, Sovereign of the Universe, who has sanctified us with G-d’s commandments and has commanded us on moving* the lulav.

בְּרוּךֶ אָתֶה ײַ, אֱלֹתְהֵינוּ מַלְךֶ הָעוֹלָם, אֲשֶׁר קִדַשְׁתַנוּ בְּמִצְוֹתֶיהֶ וְצִוְתָנוּ לָשיב בָּסוּכה
B’rucheh Ateh Yah, Elot’heinu mal’cheh ha’olam, asher kidash’tanu be’mitzvoteh’eh ve’tziv’tanu lasheyv ba’sukkah.
Blessed are You, G-d, our G-d, Sovereign of the Universe, who has sanctified us with G-d’s commandments and has commanded us to sit in the Sukkah.

De-personified:
בְּרוּךֶ אָתֶה ײַ, אֱלֹתְהֵינוּ ​רוּחַ​ הָעוֹלָם, אֲשֶׁר קִדַשְׁתַנוּ בְּמִצְוֹתֶיהֶ וְצִוְתָנוּ לָשיב בָּסוּכה:
B’rucheh Ateh Yah, Elot’heinu ruach ha’olam, asher kidash’tanu be’mitzvoteh’eh ve’tziv’tanu lasheyv ba’sukkah.
Blessed are You, G-d, our G-d, Sovereign of the Universe, who has sanctified us with G-d’s commandments and has commanded us to sit in the Sukkah.

Blessings from R' SAM Luckey; de-personified by SOJOURN staff.