I think it is clear that if a Muslim had shot a member of a different religion and their newsfeed was found to be hateful toward other religions, people would not hesitate to assume that it was likely religiously motivated, which wouldn't be an unfair assumption. It's not an unfair assumption to assume this was religiously motivated either.
Rest in peace to the victims and may the lesson be one of nonviolence from all sides.
I think that would be a simplification. I wouldn'talways jump to the conclusion that a Muslim terrorist hating another group would necessary be a Islamic terrorists or that religion would be their primary motivation. The Palestinian terrorists in the 70-80ties, may usual have been Muslims, but they was not really Islamist, just as IRA wasn't "Catholist" (or whatever you wanted to call a ideology of fundamentalistic Catholism). Yes this guy clearly didn't like Islam or Muslims, but you really don't need a religious (or in his case areligious) motivation to dislike obvious Muslims, sometimes it's just a dislike or hatred of the other, other times it's based on personal experience (I for example doesn't blame holocaust survivours who don't like Germans).