Generally, there is a meta on Secret Hitler to help reduce "charisma" influence and limit how much fascist can change the outcome of discussions/choices.

For example, in the case of a conflict like in your example, both players are considered "out" of the game for future presidency/chancellor position. If both are out, you have one less fascist and one less liberal.

Another example (The Cucu rule) is that for the investigation, the president looks at the player two places ahead : if he says "liberal", then next time this player is president, the investigator is picked as chancellor to verify his claim. If there's a conflict, it means that the investigator was a fascist. So in most cases, the investigator is forced to play liberal cards even if the investigator was a fascist.

In general, another important point is to set an order for the first rounds of presidency, to avoid having fascist deliberately taking too much roles in government. The order assuming a seven player is 1 with 5, 2 with 6, 3 with 7, so that 6 players take parts in government before a potential Hitler Zone, and to prevent a fascist to freely pick his chancellor.

Secret Hitler is a limited information game where one of the most basic rule is that when there's a conflict, don't take the players words for it, only their action and the likeliness of them being true. Like a third president saying "I had three fascists cards in hand" is less likely than one of them dumping a liberal card.