Does it make sense to broadly interpret right wing politics, both then and now, as literally "reactionary" to left wing ideas?
No, more often reactionary to societal change in any shape or form and, most importantly, instability.
In France for example, two of the most important at right thinkers Maurras and Barrès reacted to industrialization and the political instability of the 3rd Republic. Maurras proposed a return to an almost feudal system of monarchy while Barrès was the ather of national socialism (which relates in no way whatsoever to Marcist thought and actively rejects Marx). Both believed primarily in these modes of government because they believed that a stronger form of governace. The third republic had an electoral system of proportional representation and this led to a lot of coalitions and unstable governments which changed often. At te same time, industrialization has led to an exodus to the cities and plthe new city dwellers lived in slum like conditions and their jobs were unskilled and poorly paid. A bourgeoisie class had emerged. These monumental changes in society led to great unrest and obscurity and couple with political instability, this led to popular far right movements which used nationalism and anti-Semitism to unite Frenchmen, give them a sense of pride and superiority and unite them against the supposed Jewish conspiracy to control politics, economics an culture.
In Spain, Franco's rise was also preceded by enormous political instability. In the previous decades Spain had worked it's way through several democracies, monarchies and dictatorships; all of which had deteriorated. The only one which had had any longevity or tabouli tu was the dictatorship of Primo de Rivera. Directly before the civil wat there were elections to establish a new democracy in Spain, the left alliance won and Franco began his conquey of Spain from Morocco. Although Franco was desperately opposed to left wing politics, he was essentially trying to install a stable, protectionsit, nationalist state which would last.
And finally, Germany. Post WWI, te Weimar Republic was notoriously unstable an the crippling financial reparations of the Versailles Treaty and the Great Depression has brought the German economy to its absolute knees. Currency was absolutely worthless due to hyperinflation, unemployment was massive, the German population were being relentlessly humiliated on the world stage. Hitler rose to power because of these circumstances.
Even now, the rise of right wing parties in Europe can be directly linked to economic instability and a big change in the racial and cultural make up of Europe, not the rise of radical left wing thought, as the far left have lost mostnd their ground in the last few decades in Europe.
Both Fascism and Communism are reactionary to the filings of the status quo, and I say this as a Marxist. While during the rise of fascism in Europe, Marxist thought also rose is no coincidence, but fascism was not birthed by Marx. Both movements react to and attempt to combat political and economic instability and become popular in periods of low national Morale, the aforementioned instability and great social change, which always sows doubt.
Sources: many years of political theory study