Evidence
1. There is a paragraph about their theme fragrance in Trivia of this document, which consists of a total of 12 flavors, and they share six. (Lemon, Lilly, Rose, Jasmine, Amber, Musk)
2. They are the characters who interact most with Rin. Sesshomaru and Kagome are always devoted to Rin, and when they are together, they are naturally for each other and do not want to pay.
3. In fact, there is no female character more friendly to Rin than Kagome. In animation episode 81, Kagome was the first to run to her in order not to hurt Rin if the Inu brothers and Kohaku fought, and also to take care of her.
4. It was the first time Kagome and Rin were aware of each other, and when Rin said goodbye to Kagome, Kagome unconsciously spoke that she is already missing Rin.
5. In animation episode 79, Kagome first realized that Sesshoumaru was accompanying Rin as his ward, and she thought it was unbelievable.
6. Since animation episode 52, they have generally maintained a friendly relationship and try to praise even if they are clumsy whenever they discover their strengths. In episode 104, Kagome tries to defend Sesshoumaru by explaining to Inuyasha that he did not hurt her and her pack.
7. In TFA episode 26, Kagome calls Sesshoumaru Big Brother. Sesshoumaru doesn't like such a disrespectful title, but he ignores Jaken, who suggests punishing Kagome, and declares that he would rather kill his faithful servant if Jaken didn't stop nagging.
This rather fluffy situation reveals that Sesshoumaru has no objection to Kagome's intimacy with him.
Published in 2013, the 35th anniversary set of Rumiko Takahashi's debut features cartoons she has shown during her 35 years in the cartoon industry. Of course, there's also the Inuyasha section, so read the passage that explains Sesshoumaru's character development process. Rin is not the only one who made Seshoumaru feel compassionate. Kagome, along with Rin, had a significant impact on his current character.