Clickable links in Mail don't work

I never thought about this before. What determines whether the PDF is rendered and displayed in Mail?

Mail will render a PDF inline if it is one page and the size is below a certain limit. Multi-page PDFs and very large PDFs will not render inline. There may be other restrictions, but I haven’t encountered those.
I also think there is no way to force not-rendering-inline of a PDF, as a sender, if you wanted to.

The problem PDF I mentioned also has clickable links in Preview or Safari. When I view the problem PDF in Mail, the links don't work.

Now I understand that you specifically mean that the links don’t work inline (where the object is rendered as part of the message). I think that may simply be a limitation of how Mail renders PDFs inline: without support for links.
Mail.app on iOS is a little bit more transparent, as a single click on an attachment will open it in a viewer (but not a separate app) that does support web links.

The solution may simply be to repeat your links in text in the e-mail message. E.g. something like: “For your convenience, the important links on the poster are: wwwfoocomlist and wwwfoocomticket”.

Make sure you create valid internet hyperlinks (Web Links), as some ‘smart’ correcting and automated detection functions may not be available on the iPhone, as they are on the desktop. Text with http, www, a​@​b.com might be automatically interpreted as a link, without such definition in the PDF, but that depends on software with the recipient that you cannot control.

The proper way may be to set explicit links in a PDF editor; the full URL with htt​p:// or htt​ps:// .

Try mailing this Apple PDF to yourself. The various text links work for me in Mail on iOS.