The modern idiom "to go straight" means to stop being a criminal and obey the law:
He decided to finally give up his life of petty thievery and go straight.
This use of "ride straight" clearly has a different meaning, and one that's old-fashioned and/or limited to British English. My interpretation without further context is that their personal and social views were simple and conservative -- they had a particular view of the world and didn't allow distraction from new "ideas" about how the world should be.
Full text of the paragraph:
Our firm, of course, has known many generations of the Crales. I knew Amyas Crale and his father, Richard Crale, and I can remember Enoch Crale-the grandfather. Country squires, all of them, thought more of horses than human beings. They rode straight, liked women, and had no truck with ideas. They distrusted ideas. But Richard Crales wife was cram full of ideas-more ideas than sense. She was poetical and musical-she played the harp, you know. She enjoyed poor health and looked very picturesque on her sofa. She was an admirer of Kingsley. Thats why she called her son Amyas. His father scoffed at the name-but he gave in.
The "rode straight" sentence is used to contrast with the following sentences about Richard Crales' wife, who is apparently a very different sort of person. My guess is that this contrast will be important to the story, at some future point.