I think it’s safe to say that Jonathan Edwards was neither a universalist nor an inclusivist.
Christ came into the world to engage in a war with God’s enemies, sin and Satan; and a great war there is maintained between them; which war is concerning us; and the contest is, who shall have the possession of OUR HEARTS. Now, it is reasonable under these circumstances, that we should declare on whose side we are, whether on Christ’s side, or on the side of his enemies. If we would be admitted among Christ’s friends and followers, it is reasonable that we should profess we are on the Lord’s side, and that we yield OUR HEARTS (which the contest is about) to him, and not to his rivals. And this seems plainly to be the design and nature of a public profession of Christ. If this profession is not made, no profession is made that is worth regarding, or worth the making, in such a case as this is, and to any such purpose as a being admitted among his visible friends. There is no other being on Christ’s side, in this case, but a being so with an undivided heart, preferring him to all his rivals, and renouncing them all for his sake. The case admits of no neutrality, or lukewarmness, or a middle sort of persons with a moral sincerity, or such a common faith as is consistent with loving sin and the world better than Christ. He that is not with me (says Christ) is against me. And therefore none do profess to be on Christ’s side but they who profess to renounce his rivals. For those who would be called Christians, to profess no higher regard to Christ than what will admit of a superior regard to the world, is more absurd than if a woman pretending to marry a man, and take him for her husband, should profess to take him in some sort, but yet not pretend to take him in such a manner as is inconsistent with her allowing other men a fuller possession of her, and greater intimacy with her than she allows him. The nature of the case, as it stands between us and Jesus Christ, is such, that an open, solemn profession of being entirely for him, and giving him the possession of our hearts, renouncing all competitors, is more requisite in this case, than a like profession in any other case. [from Humble Inquiry Concerning the Qualifications for Membership in the Visible Christian Church]