My father is very conservative as well, and never had nice things to say about the LGBT community. At first when I told him, he was emotional about what I went through keeping things to myself for all these years. But after that initial period there were several months of where he would refuse to discuss anything and acted very distant. He still won't refer to me by female pronouns or by my female name. But he has lately warmed up to the whole situation, and has slowly begun to accept things. I think that as parents their kids are a reflection on them (I'm not a parent BTW), so being a macho guy's guy, and having a son who'd rather be a girl must've been difficult to accept. I think my dad was concerned about how the rest of the family and his friends would think about him. Since pretty much everyone knows about me and has been accepting, things have not been as difficult as they were before.
One of the reasons I waited as long as I did before coming out was because of my fear of my father's reaction. And I knew as I was getting ready to tell him that things would probably change between us (and they have). Lately though we have talked about things a little more, and even though he's told me how weird the situation is, he's trying. Hopefully with time, things will get easier and it won't have to be as difficult as it has been.
I guess it comes to the point where you have to bite the bullet and see what happens. Acceptance might not happen immediately but opinions change over time.