Was The Reverse Flash gay?

There has been nothing stated about Eobard Thawne's sexuality in-universe or out of universe at this time. The character is all about ambiguous actions, playing his cards very close to the chest, for obvious villainous reasons. His love/hate reactions to Barry being the most blatant (he "respects" Barry but you know, still wants to kill him). If anything, his actions show that he is a pragmatist and very calculating. He's playing a long game in order to kill Barry while still being able to get back to his own time. He's likely just playing it up as needed, like pretending to be paralyzed, until it's no longer useful. We know that he's been ready to get out of the chair when his life is at risk (when the robotic bees swarm the headquarters).

Then again, he is from the 22nd century (25th in most comics), who knows what sexual identities exist five generations from now (2155).

Of course, comic Hartley, in the New 52 reboot from 2011ish, was tied to a relationship with Captain David Singh, who is confirmed Gay, and eventually married to Rob, in the series. The Draft script of the Pilot has Hartley still with Team Flash, stating that he, not Cisco, designed the firefighter suit, while dating a fireman. So the ho-yay feels might come from Hartley. Coincidently, the actor Andy Mientus is also openly Bisexual.

Feelings are not always for lovers. Sometimes they are for your family and friends too.

Eobard Thawne was not as selfish as we suspect but on the other hand he have affection for many people. Like he stood against Eiling for Grodd. He told Cisco that he always thought of him like his son. He left a video proof for Allen etc. etc.

Arrow/Flash have never been shy in showing LGBT theme, so why would they do this with Thawne?. I think it was just affection for Hartley too which you have mistaken for love.

But as proved time by time Thawne has always put his mission above any affection or people. Same he does with Hartley.

I don't think Eobard had romantic feelings for Hartley, more of a father/son mentor bond. I think he had great admiration and pride for Hartley but nothing sexual or romantic. He might have been gay, bisexual or straight. I'm going for straight purely on the fact that he never showed any romantic interest, none at all for males. Now, you could put this down to him being a generally secluded person or you could say that he was simply heterosexual. This is proven when he states that he still gets "teary eyed" over Tess Morgan's murder. Again this could all be simply because he absorbed the real Harrison Wells' DNA but and therefore gained some of his emotions and memories. All in all in my opinion I believe Eobard Thawne to be generally Asexual, seeing as he seems to feel no personal attachment to anyone romantically, the only time that showed him with any romantic feelings were simply because of someone else's emotions inside his own brain. So yeah, I believe Eobard to be asexual and generally a blank canvas with relationships

DC's Wikia Entry for Thawne definitely indicates that he tried to romance a woman who rebuffed his advances. This is not definitive evidence that the TV version of the character was not gay, but potentially a strong (if out of universe) indication of any leanings. Given that he's clearly a psychopath, it's possible he's entirely asexual.

Eobard fell in love with a reporter named Rose who had been hired by Central City Science Today to interview him. However, he learned that she was engaged. His future self interfered yet again, killing the Rose's fiance and eventually every man who she had ever dated, when she steadfastly refused to believe that her fiance was gone for good. They became platonic friends; however, she continued to rebuff Thawne's romantic advances, eventually retaliating physically when he attempted to kiss her. In anger, his future self traumatized the reporter as a child, rendering her mute and causing her to be institutionalized for the rest of her life.