The mutual language was made artificially, in the sense its naming was political. It was a political construct as much as the Croatian language is a political construct. They're not identical languages and people in general do not consider some exact degree of difference as decisive, even if (some) academics do. It's not like calling the earth flat since that is not a matter of degree.
For example, Dutch is derived from, and similar to, German as is Swiss German, but no-one is saying that Dutch should be called Dutch German, and the Dutch would surely vigorously object to that. Croatians have every right to reject the notion that they speak Serbo-Croatian or that such a language even exists.
Can you say there's only 10% difference between the two languages? Absolutely. Does that give someone the right to declare the languages the same outside of Academia? No. There is no objective standard to rest your claims of objective truth on.
Let's continue tying the Dutch into this discussion. The war crimes tribunal for the former Yugoslavia was in the Hague. One of the official languages there was BCS: Bosnian/Croatian/Serbian. Not three of the languages, but one of the languages. Can you imagine anything more damning than being charged in a court of law, and not understanding the charges? Fortunately this was not the case, as the languages are in fact identical. That a court of law sees them as identical is a very objective standard. There are many other examples.
You are also doing Croats a disservice by presenting them as a hive mind that rejects certain notions in unison. Some of them disagree explicitly that the languages are separate, and a lot of them disagree implicitly (if not most!). For example, only a couple years after the war there was a Serbian movie in Croatian theatres, and it was subtitled. This was met with widespread ridicule in Croatia, and the practice has been, as far as I know, abandoned. So even if people don't want to open this can of worms (that I unfortunately did here), when faced with the full consequence of it, a large number of them will find it ridiculous.
To be clear, I am a native speaker of this language, or if you wish languages. I also speak English and German, and have spent some time in Switzerland. I believe my experience is adequate to say that we are in fact speaking one language, and the differences are nothing more than regional differences, that exist everywhere else in the world.
For example, Dutch is derived from, and similar to, German as is Swiss German, but no-one is saying that Dutch should be called Dutch German, and the Dutch would surely vigorously object to that. Croatians have every right to reject the notion that they speak Serbo-Croatian or that such a language even exists.
Can you say there's only 10% difference between the two languages? Absolutely. Does that give someone the right to declare the languages the same outside of Academia? No. There is no objective standard to rest your claims of objective truth on.