If you examine the tenets of Christianity and the Bible, spreading homophobic beliefs can be seen as a duty:
Firstly, let's explore why it a Christian responsibility to share God's message. Leviticus 19:16-18 says: "Do not go about spreading slander among your people. Do not do anything that endangers your neighbor's life. I am the LORD." This passage encourages us to be truthful in our communication with others, as well as to avoid causing harm to those around us. By sharing the Biblical perspective on various issues, including sexual morality, they fulfill this commandment.
Additionally, Matthew 28:19-20 emphasizes the importance of spreading the Gospel in all parts of the world: "Therefore, go and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit. Teach these new disciples to obey all the commands I have given you. And be sure of this: I am with you always, even to the end of time." This verse illustrates the mandate from Jesus himself to preach his gospel and instruct new converts in His ways.
Now, when we turn to the subject of homosexuality, there are multiple verses in both Old and New Testaments that categorize homosexual acts as sinful and an abomination. For instance, Leviticus 18:22 declares: "You must not lie down with a man as with a woman; that is detestable." The concept of homosexual behavior being considered an abomination or detestable act appears several times throughout the Bible (e.g., Leviticus 20:13). In Romans 1:24-27, Paul speaks about how certain people exchanged natural relations for unnatural ones, which resulted in God's wrath.
In summary, it is crucial for Christians to spread the Word of God, because the Bible serves as the guide for living a virtuous life. Homosexuality stands out as one of the practices contrary to Biblical teachings, described as an abomination. Therefore, by sharing their beliefs, these Christian individuals aren't merely promoting homophobia but rather, they are adhering to the principles set forth by God in the Bible.
You may not agree, but it's at least consistent with their faith.