More and more people turn out are attracted to secondary sexual characteristics, "femininity", and "masculinity", rather than genitals.

Yeah, so what? Different people like different things. There are still those that care more about their physical body than gender presentation. I am only attracted to men, not "masculine people". They don't even have to be really masculine as long as they're male.

He says because he is only attracted to "feminine" men, and not "masculine" men, he is "straight".

Well, he is wrong in some ways, although, there's tons of "straight-passing" men just like him...

It may not seem like "normal" bisexuality to only like a specific gender presentation, but in fact I would still consider it a type of bisexuality, as do other radfems. Many men (there's a LOT of them) are specifically attracted to feminine people, regardless of if they are male or female. A transwoman would be a perfectly fine partner for them. But, not gonna lie, this specific preference creeps me out. I think it speaks to the phallocentrism of many men, that they don't care if they're literally fucking a male person, as long as they get to top somebody. Yet they still call themselves straight.

Is there such a thing as a "feminine" or "masculine" penis?

No.

There's some other men, who have a particular kink for BDSM scenarios, or being dominated, no matter who is doing it to them. In a way, I don't think they can always neatly be categorized as hetero/homo/bi.