Short Answer: One can BOTH respect the rights of others to hold "abominable" beliefs while at the same time not accepting those beliefs as truth.  It is wrong to assume that the words from the First Vision are marching orders for an attack against the false denominations and abominable creeds that it mentions. Such an assumption would be a very serious, foolish, and WRONG takeaway because we are engaged in a battle against not just one evil, but three:

Longer Answer: Strong convictions often lead to religious intolerance and political tyranny. For this reason, the Restoration requires not only strong convictions pertaining to RELIGIOUS TRUTHS, but equally important strong convictions pertaining to RELIGIOUS TOLERANCE and RELIGIOUS FREEDOM. The same religious rights and freedoms that protect all other sects also protect the Latter-day Saints. Without these rights and religious freedoms, the religious truths associated with the First Vision would never have seen the light of day due to religious intolerance and political tyranny. Joseph Smith himself wrote:
"I have the most liberal sentiments, and feelings of charity towards all sects, parties, and denominations; and the rights and liberties of conscience, I hold most sacred and dear, and despise no man for differing with me in matters of opinion."

Here is the longer article that prompted the question as we were writing it: Top 5 Takeways From Joseph Smith's First Vision

Here are some great quotes from churchofjesuschrist.org articles:

Elder Dallin H. Oaks: Balancing Truth & Tolerance
"In the balance between truth and tolerance, tolerance can be dominant where the behavior does not involve us personally." ...
"We must stand shoulder to shoulder with other believers to preserve and strengthen the freedom to advocate and practice our religious beliefs, whatever they are." ...
"Finally, the spirit of our balance of truth and tolerance is applied in these words of President Hinckley: "Let us reach out to those in our community who are not of our faith. Let us be good neighbors, kind and generous and gracious. Let us be involved in good community causes. There may be situations where, with serious moral issues involved, we cannot bend on matters of principle. But in such instances we can politely disagree without being disagreeable. We can acknowledge the sincerity of those whose positions we cannot accept. We can speak of principles rather than personalities."

Church Newsroom: Interfaith Relations
"It is important to note that interfaith cooperation does not require doctrinal compromise. Though the Church asserts its ecclesiastical independence and recognizes its doctrinal differences, this does not prevent it from partnering with other faiths in charitable projects. These efforts are based on universal values. A different interpretation of the atonement of Christ, for example, need not diminish the mandate of Christ to "love thy neighbor as thyself." Therefore, it is necessary to maintain a separation between charitable efforts and doctrinal tenets, while at the same time sharing mutual concern for those in need. People of good faith do not need to have the exact same beliefs in order to accomplish great things in the service of their fellow human beings."