The Scottish Tory leader said she had asked for, and received, a "categoric assurance" from Mrs May that any arrangement between the Conservatives and the DUP would see "absolutely no rescission of LGBTI rights in the rest of the UK".
Her aides are said to be working on a deal that would see the Scottish party break away to form a separate organisation.
Many commentators focused on the DUP vetoing the introduction of same-sex marriage in Northern Ireland in 2015, in opposition to the rest of the United Kingdom, and in stark contrast to this country which voted in favour of same-sex marriage in a referendum.
Ruth Davidson has dismissed a suggestion she will seek to break the Scottish Conservatives away from the United Kingdom party following a humiliating General Election result for Theresa May.
Speaking on the BBC's Good Morning Scotland programme he gave the example of the Scottish fishing industry which is anxious about Brexit negotiations.
That put them ahead of Labour and closed the gap to the SNP - who had a bad night, losing 21 seats including their Westminster leader Angus Robertson and former Scottish First Minister Alex Salmond.
Ms Davidson said: "I was fairly straightforward with her and I told her that there were a number of things that count to me more than party".
They are opposed to LGBTI equality at large and have been holding up same-sex marriage in Northern Ireland, although there is a majority for it.
In a short statement outside Downing Street after an audience with the Queen, Mrs May said she would join with her DUP "friends" to "get to work" on Brexit.
Ruth Davidson has given Sinn Fein- and Jeremy Corbyn- a stick with which to beat the fledgling Conservative-DUP partnership in its infancy period.
But Ms Davidson, who led the Scottish Tories to their best result since 1983, said that was "not enough" and demanded Ms Sturgeon immediately dump a plan she said had turned out to be "a massive political miscalculation".
Ms Davidson responded by tweeting: "Folk might remember I fought a leadership campaign on the other side of that particular argument".
The DUP are pro-union (not Europe but UK), pro-Brexit and socially conservative.
The Scottish Tory leader hopes to convince the DUP to allow same-sex marriages in Northern Ireland.
Battle for the city of Marawi now in its third week as thousands flee. "They are just providing technical support", he said. In 2002, the U.S. helped Philippine authorities track down Abu Sayyaf leader Abu Sabaya, who was killed in that operation.
However, the Qatari foreign minister downplayed the likelihood of military conflict. "They are hosted here. for peace talks". He stressed that Qatar's strategic choice was to solve any crisis through dialogue, Qatar News Agency (QNA) reported.
The watchOS 4 will be available as a free update to the Apple Watches that can be paired with iPhone 5s and later on iOS 11 . There is also a Activity coaching, GymKit for Apple Watch to communicate with Gym equipments and a new music experince.
Steve is so deep in the mythology that after some debate we found that just like Wonder Woman needs Steve, we needed Steve too. With Jenkins now a proven commodity, she could potentially demand a much higher payday to come back for another film.
With the highly-anticipated stand-alone Wonder Woman film hitting theaters this weekend, talk has already begun about a sequel. Perhaps that's exactly why this superhero movie didn't include one - it might just be that Wonder Woman is its own movie.
Victor has been indicted by a federal grand jury on a single count, but the government said it would likely add to the indictment. Because of her training, the indictment contends, victor knew disclosure of the document could endanger national security.
These new, more powerful iMacs represent Apple making good on a vow to introduce PCs that cater to the professional market. The rest of the Mac line will also be getting the Kaby Lake processor up to1.3 GHz Core i7 with Turbo Boost up to 3.6 GHz.
Gallagher, formerly of Oasis, earned loud cheers from the audience as he emerged in his home town in surprise form. Other performers will include Pharrell Williams, Usher, the Black Eyed Peas , Robbie Williams and Niall Horan.
New smart speaker expected as Apple kicks off conference
That device was just a multi-touch feature phone with a few Apple utilities until it became everything with the App Store launch. Against other smart home assistants, the HomePod's targets are different from ostensible competitors like the Amazon Echo .
Eric Trump calls father's critics 'not even people'
And as Forbes points out in its report, "Altruism as a business-development strategy isn't necessarily illegal". Overall, he added , the foundation's efforts have yielded 'over $16.3 million dollars for the children of St.
Senate Republicans Homing in on Final Health Bill
The small print taketh away. "I'm very encouraged, very encouraged". "I'm not going to go into details". Ted Cruz, Texas Republican, defended the process, saying it fostered comity among Republicans.
What is Hillary Clinton thinking?
It nearly defied belief to watch Hillary throw the Democratic National Committee under the bus - which she did with a vengeance . Give Clinton (or one of her lackeys) credit for this comeback, a play on Trump's mysterious new pet word.
CBS Says It Will Air Comey Testimony
No". "I think you'll see her take a larger role in the month of June", said Short, "to draw attention to this dilemma". Asked at a news conference if he pressured Comey to drop the Flynn probe, Trump had said, "No.
All 4 Yankees home runs in 8th inning vs. Blue Jays
Pineda gave up a hit to Luke Maile , a career.178/.208/.297 big league hitter, in an 0-2 count with a pitch up at shoulder level. Biagini retired 10 batters in a row until Castro led off the seventh with a bloop double to left.
Rahal wins Detroit IndyCar opening race
It put us up where we belonged and I think we showed that the No. 5 Arrow vehicle had a lot of pace. Today was great for points. "Tires are the name of the game here", Hinchcliffe said.