US Supreme Court ruling issued in Lawrence v. Texas struck down all sodomy laws on the basis of privacy and liberty. The decision overturned any laws remaining in all US states which prohibited acts of sodomy.

Governor Mark Dayton signed a bill into law overturning a previous law which banned marriage between anyone other than one man and one woman.

No conditions required. Non binary options on drivers licenses pending.

Joint adoption is not explicitly prohibited, though no formal law states it is legal, and no state court has ruled on the issue. Second parent adoption by a same-sex partner is not explicitly prohibited by state law, and several lower courts in Hennepin and Atkins counties have allowed second parent adoptions to take place.

Language specifically protects on the basis of sexual orientation and gender identity. Exemptions exist for religiously affiliated/operated organizations.

Language protects based on sexual orientation and gender identity. Religious exemptions apply.

Discrimination on the basis of sexual orientation and gender identity is illegal. Religious exemptions apply.

Additionally, the Human Rights Campaign states, "The Department of Housing and Urban Development (HUD) requires grantees and participants of HUD programs to comply with local and state non-discrimination laws that include sexual orientation and gender identity.
HUD also prohibits inquiries regarding the sexual orientation or gender identity of a prospective tenant or applicant for assisted
housing in every state (March 2012)."

Don't Ask, Don't Tell is officially repealed throughout the United States, and gays and lesbians may openly serve.

No

Ban on blood donations from MSMs applies to any man who has had sex, even once, with another man on or after January 1, 1977.

Conversion Therapy is currently legal in Minnesota, and has reportedly been carried out at various clinics throughout the state -- perhaps most notably at the clinic of Congresswoman Michelle Bachmann's husband, Marcus Bachmann. No law currently bans it, though a meager attempt to introduce a ban has taken place. The proposed ban would only impact minors (Those under the age of 18). Though it's not actually ambiguous (It is in fact legal), this is the best indicator of the available options.