Historically virtually all cultures have been against gay people, outsiders, and women challenging male superiority. It’s in the name. Conservatives offer to keep things the way they are. People are instinctually afraid of the unkown, even if what they know sucks—they can deal with it, and to a lot of people that sounds better than being lead into the potentially unknown by those who propose that change is for the best.
Most people are not complete intellectuals. They will not override their instincts in pursuit of what they think to be right. The conservative political groups in almost every country have a strong footing, even if they can seem unwieldy and delusional (even to their own), because they derive their persuasional power from being able to exploit that very basic instinct.
People of different cultures are unknown. Many interpret their presence as an attempt to change everything. Homosexuals have not been historically accepted by any culture. Women have historically not had the same credit and allowance of rights as men. To allow for these things is to change a culture in a lot of fundamental ways, and the results are unpredictable. It’s likely nothing would happen, but people tend to think the worst.
Mankind is remarkably adaptable when the situation calls for it, but it will also resist change for as long as it possible can. Conservativism is in our nature. It sounds like a good deal to anyone, liberal or conservative, but often times keeping things the same is unrealistic or impossible.