A phobia doesn’t HAVE to be a mental illness- the suffix can also be used to mean “aversion”. A lot of cell phones have screens with an oleophobic coating, for example, but they’re not afraid of grease. I don’t think fear of or aversion to Islam is an unreasonable response, given the events of the past 1,400 years.
The difference between examples of violence or alleged misogyny in the Bible and the Qu’ran is that while the Bible commands the Israelites to drive out the Canaanites from the land, that’s a time and place and people limited event. We can learn from it, certainly (the Fathers used it as an allegory for the vigor in which we must drive out sin, with Joshua as a type of Christ), but it’s not a command for Christians to commit violence against non-Christians indiscriminately. Indeed, “all who take the sword will perish by the sword.”
To contrast, the Qu’ran, hadith, and sira are replete with injunctions urging Muslims to make converts by force. Islamic apologists will often point to earlier, Meccan ayat in order to appear peaceful, but these are abrogated by the chronologically later Medinan suras.
Examples: 9:5 “Then, when the sacred months have passed,
slay the idolaters wherever ye find them,
and take them (captive), and besiege them, and prepare for them each ambush.
But if they repent and establish worship and pay the poor-due, then leave their way free.
Lo! Allah is Forgiving, Merciful”
2:191 “And kill them wherever you find them, and turn them out from where they have turned you out. And Al-Fitnah [disbelief or unrest] is worse than killing… but if they desist, then lo! Allah is forgiving and merciful. And fight them until there is no more Fitnah [disbelief and worshipping of others along with Allah] and worship is for Allah alone. But if they cease, let there be no transgression except against Az-Zalimun (the polytheists, and wrong-doers, etc.)”
4:74 “Let those fight in the way of Allah who sell the life of this world for the other. Whoso fighteth in the way of Allah, be he slain or be he victorious, on him We shall bestow a vast reward.”
Bukhari (52:260) - "…The Prophet said, ‘If somebody (a Muslim) discards his religion, kill him.’ "
Examples are easily multiplied. See how Mahomet treated the Banu Qurayza.