Tony Wills, in A People For His Name (pg 100) says:
Volume Seven (of the Studies in the Scriptures) opposed the war. It termed patriotism "a certain delusion" and "in reality murder, the spirit of the very Devil", and "a narrow-minded hatred of other people". It also quoted a great deal from Reverend John Haynes Holmes who was viciously persecuted at about the same time for advocating pacifism. At about the same time General Bell of Long Island visited Rutherford to get his followers to submit to military service. Rutherford refused to do so. He wrote letters of advice to Bible students in the camps advising them not to don a uniform nor do anything even closely connected to the military. These letters were intercepted by the censors. All these factors added up to considerable opposition to the Bible students by the authorities.
Wills doesn't cite his source for the letters, but they may be the same as those quoted by Leolaia.
Also see WT March 1918, page 6221-2 reprints:
We are not against the Government in any sense of the word. We recognize the Government of the United States as the best government on earth. We recognize that the governments, being political and economic institutions, have the power and authority, under the fundamental law, to declare war and draft their citizens into military service. We have not the slightest disposition to interfere with this, nor to speak against it so far as the governments’ power or authority is concerned. We recognize that it is the duty of every citizen to obey the laws of the land, and the duty of every citizen, who can conscientiously do so, to participate in the defense of the country. All should be respectful to officers of the law. (Acts 23:5) The law the land recognizes that there are Christian people who cannot engage in military service without doing violence to their conscience. Hence the Congress of the United States, in passing the Selective Draft Act of May 18, 1917, inserted a clause providing that certain ones, under certain conditions, should not be compelled to engage in combatant military service. We hold that the members of our SOCIETY come within the purvue of this section of the law and are entitled to its protection. And none of our members, so far as we know, have done more than to claim the benefit of the provisions of this Act of Congress.
On May 15, 1918, (WT 6261R) an article "Non-Combatant Service Defined" explained how Bible students could claim exemption from the draft. The article concluded:
It is not the province of THE WATCH TOWER to tell any one what he should or should not do; but we can and do say that every Christian should be obedient to the law. The order of the President is a part of the Selective Draft Law. Where one in good faith has applied to the Local Board for classification and the Board has not issued to him a certificate granting non-combatant service, then when called he should readily respond to the call by going to the cantonment and presenting himself to the commanding officer, who, under the President’s order, has the power and authority to issue to him a certificate assigning him to non-combatant service. The President further provides that it is the privilege of such conscientious objectors to request assignment to some branch of non-combatant service aside from the Medical Department.
Rutherford may have written letters to Bible Students advising them against going to war, but in official publications, certainly at that time, he was much more circumspect, advising them only to take advantage of the legal avenue of claiming to be a conscientious objector.