That's a lot of mental gymnastics. And I know it well, because as a christian for 30+ years of my life, I played those mental gymnastics too. I now look back at that time of my life and how I thought and am ashamed of it all.
If someone commits a criminal assault against someone else, then it's just a criminal assault... unless the motive was hate (for example, they did the assault because they (or their god) hates gays, or they (or their god) hates jews, or they (or their god) hates mexicans, etc, etc...), and then the criminal assault also becomes a hate crime. It's not the action that makes it a hate crime. It's the motive of hate that does.
This is not limited to crimes. If someone does action ABC, then it's just action ABC... unless the motive was hate, and then the action ABC becomes a hate action ABC. (note, I"m not speaking in the legal sense, but just in general how not all actions are motivated by hate, but some are).
You can do all the mental gymnastics you want with sin, sinners, love, hate, god people, etc, etc... but none of that matters. Because it's all meaningless to the victims. LGBTQ people get treated the way they do because some religious people believe homosexuality is a sin, and god hates sin, so because of this they are choosing to treat LGBTQ with negative actions. And given the motive is hate, their action is a hate action. It's doesn't matter if the action is something extreme like burning down LGVTQ homes, or something as simple not hiring them, making a cake for them, or allowing them to participate. Their action, whatever the degree of action it is, is a hate action.
The whole "love the sinner, hate the sin" mentality is nothing more than a way believers try to resolve it all in their own minds. But to the victim, it's meaningless. If god hates homosexuality, then in their eyes god hates them, because what they are is homosexual. They didn't make that choice anymore than you chose to be heterosexual (assuming you are). It has nothing to do with free will. it's not a choice. So if god (and by extension you by your negative action) hates homosexuality, then the homosexual is hated by god (and by extension you), because THEY ARE WHAT GOD (AND BY EXTENSION YOU) HATES!!!