It's more than that, I would think:
Ok so let's begin. Conservative parties are right-wing and they, with the elites (many of whom were large landowners, Junkers), retained their power after 1914. So throughout the Weimar Republic's days under Eber they retained influence, especially in the army and they retained prestige by purporting myths about the new goverment and blaming them for the harsh Treaty of Versailles - the terms became great propaganda for them. (The army leadership was conservative as well.)
THEY OPPOSED the policy of rulfilment which the Democratic Party and the Social Democrat's had followed (implemented by Ratheneu who was assassinated)... until they missed the reparation in 1923 and then in 1924 Stresemann negotiated for loans, French withdrawal and a lax in the future on repayment under the Dawes Plan.
Many undermined the democratic process, extreme right-wingers did not believe in the republic and promoted the Dolchstosslegend, 'stab in the back legend' about Bolsheviks and Marxists and the Weimar government. The Weimar government made a critical mistake, but one needed for self-preservation, with the Freikorps, who were also conservatives, because once they had tried to disband them, they turned against the government and that was the Kapp Putsch. Here the army proved that it would not act against right wing extremists as it had against the communists - which perhaps contributed to Hitler's decision to work within the realms of the constitution to ironically, undermine it. Though also the failure of his 1923 Beer Hall Putsch contributed to this.
These conservative parties and the elites supported the government chiefly during the economic instability, because of the threat of the communists (left-wing) and the growth of the KPD who they feared. The installation of Hindenburg as President at Ebert's death is not so straight forward, because it did two things. It did give the conservatives more power, and mean that the prestige of the German army continued to grow. However it also gave the republic legitimacy to some conservatives, especially as Hindenburg used his name and prestige to give it credibility and worked within the realms of the constitution.
I wouldn't say that because Hindenburg was conservative that he installed Hitler. Hindeburg was very distrustful of him. But there can be no doubt that he and Papen underestimated his ability, and certainly Hindeburg's death could never have been foreseen. Remember however, the Hermann Goerring also played an important role as Prussian Minister for the Interior, controlling half the police across Germany and being able to suppress the left-wing movement, which had always been feared by the conservatives and this move was popular amongst many people. (not the communists though, of course.lol )
Many conservatives were nationalistic. They played on desires to reverse the terms of the Treaty of Versailles and regain Posen, reoccupy the Rhineland, Sudetenland, Czekoslovakia and have an Anschluss with Austria. They also saw the new Weimar cultural change; the expressionism, Koerperkultur, freedom as morally corrupt and some historians argue that this was a view shared by many Germans. These same Germans were also distrustful of the democratic system and the emergence of this cultural movement in cities such as Berlin was seen as a result of their lax, as were the rising riots, economic instability, party police brutality (each party had their own private army) etc. etc.
Please correct me if I'm wrong on anything here. I'm still going over everything so I apologise for the lack of dates etc.
I would argue though that conservative parties and elites did play a role in the fall of the Weimar republic, but that it was a mixture also, of economic and social instability, dissolutionment after the 1923 hyperinflation and emergence of this new 'decadent' culture as many Germans saw it, constitutional flaws such as Article 48 and proportional voting, the harsh terms of Versailles, the skill of the Nazis and miscalculations by Schleicher and Papen (could be categorised under political rivalry) which led to Weimar's demise.
I would mention all of these... also some of the determinist and structuralist historians... Ian Kershaw and co. etc.
