If by agenda you mean advocating for LGBT rights, then I guess so.
This isn't a one-sided issue. Those opposed have legitimate concerns that those advocating for ignore or, worse like the SPLC, attack without regard for debate or reasonable discussion.
The anti-abortion movement has a history of violence.
So? The majority of those opposed to abortion to one degree or another are non-violent. That aside, it is just one issue of many Leftist / Progressive issues that the SPLC takes on to generate their "Hate List."
Yes, it was. Their Hate Map and the definitions of groups attached to it--or even individual persons in some cases--is the embodiment of the SPLC's hatred. They are implying those groups are worthy of violent opposition.
Not a fallacy. It's a simple question. By saying yes, then applying your logic you hate those Christians.
It is. You used a mote and bailey. You took an isolated, small group that is extremist as your example wanting me to agree with your position--which is correct for that small, isolated group--the "Mote." That is, it makes an easily defended position to base your case on. You then apply the "bailey" to it which is the much larger and difficult to defend position of all other cases.
As for your counter argument above, that's not true either. If I agree with you that the Westboro group is opposed to LGBT that doesn't mean I vilify them or "hate" them. What distinguishes the SPLC as a hate group is they take their position to the next level. They publicly out some group, or even single person, put that group on their hate map, add commentary often in the form of opinion, and then widely disseminate that. In doing so, they make the group a target for often violent opposition.
In doing all that, the SPLC is effectively generating the hate by their commentary. The SPLC also is selective about which groups they target. They rarely, if ever, target any group on the Left. They handwave, ignore, or dismiss such groups with equivocation and weasel words.