Sorry the source is my brother who worked at the FSI, and every single is not really correct because of edge cases, but that's the officers and the people at the FSI talk about it. Some countries speak more than one language, some speak English (which all Foreign Service Officers are already required to speak), and in some countries there are many positions where you will be almost exclusively dealing with English speakers even if it isn't widely spoken there (some positions in Iraq). And finally not all postings are really what you'd think of as being a "diplomat" (dealing with Americans who lost their passport for example).
Each posting has a number of language designated positions, which range from 90% of the total positions in Columbia to 8% in a Iceland (where English is almost universally spoken).
In this example at least 90% of the officers in Columbia are required to speak Spanish (and it's likely that most of the other 10% do as well). If there aren't enough people proficient in a language they will train more at the FSI. In most countries language designated positions are the majority.
So yes it's not strictly required to speak Spanish to be posted in Columbia, but you're only going to be able to get one of the 10% of non language designated positions which aren't likely to be positions that we would think of as diplomatic work.
Additionally when you join the Foreign Service you have 5 years to become proficient in a Foreign Language before you get forced out, and during that time you can only serve in the limited non language designated positions.