There problem here is that alpha (transparency) is applied twice when you first draw to a render-texture. You can play with clear values, the result will never be the same.
The only way to have the same result is not to apply alpha when you draw to the render-texture:
renderTexture.clear(sf::Color(0, 0, 0, 0));
renderTexture.draw(sprite_1, sf::BlendNone);
renderTexture.display();