I don't understand how you got that at all. The impression I got was the synthetic mathematicians were wary of applying the new "analysis" methods because lack of rigor made them question how safe and valid it was to use.

> Using another set of metaphors: Analysts followed the fast flights of their feverish and uncontrolled imagination, while synthetics kept their feet on the ground. Their procedures were slow but safe.

> I don't understand how you got that at all.

The word "reactionary" appears multiple times on that page, in association with either synthetic mathematics itself or the politics that's said to be closely connected to it. I'd say that's by far the most unambiguous part of my argument about this text.