The Bernadottes married well and the current king is not only the heir of the line from Carl XIV Johan (=Jean Baptiste Bernadotte), he is also the heir general of Gustav IV. So even though the Bernadottes replaced the previous Holstein-Gottorp-Vasa line they managed to become the heirs of that line by the marriage of Gustav V to Victoria of Baden.
no doubt the result of their mother being a Bavarian princess and their father a respected man even though he was Napoleon's stepson.
They never really mingled with other royal families, either, since they chose to intermarry mainly with nobles. Until the 1999 marriage of Princess Caroline and The Prince of Hanover, the closest thing to a royal match was that of Princess Florestine and Wilhelm, the 1st Duke of Urach, a morganatic member of the house of Württemberg. So despite being a reigning dynasty, the Grimaldis have not generally been well-regarded, throughout the good part of their long history. As it was, their stock rose over the years only because the house has managed to retain its sovereign status, while other dynasties in Europe got deposed as a result of wars or conquests. If I understand correctly, the Monégasque princes had a difficult time in getting invited to foreign royal events before the 20th century.
And if it came to that, the reason Prince Rainier III didn't invite other European royals to his 1956 wedding to Grace Kelly was that he knew they likely would snub it.
The principality of Liechtenstein has been in a somewhat similar situation. Despite being a sovereign house, the members have traditionally lived like foreign nobles at the imperial court of Vienna, as subjects of the Austrian emperor (indeed, like the Monégasques, they have largely intermarried with nobility, not royalty). That was the whole reason why the 1903 marriage of Archduchess Elisabeth Amalia (niece of Franz Joseph) and Prince Aloys was initially thought of as a mésalliance. But in the end, one can't argue with the facts: the princely house of Liechtenstein was, and still is, clearly sovereign. As it was, the emperor had to personally attend the wedding himself, in a spirit of solidarity with the bridal couple, to underscore this very fact. If you ask me, question marks were raised in large part because the marriage took place only after the controversial 1900 morganatic union contracted by the same emperor's nephew, Archduke Franz Ferdinand (half-brother of Elisabeth Amalia) and the Bohemian Countess Sophie Chotek (who would have been a perfectly acceptable dynastic bride for a Liechtenstein prince).
So not even the sovereignty of a house has necessarily guaranteed unqualified acceptance of its members as *royals*. From a purely SOCIAL standpoint, they can find themselves snubbed by other royals as *inferiors* or *unequals*. But like I said, there is nothing like retaining a sovereign status for the stock of a house to rise: Liechtenstein, too, has enjoyed a tremendous surge over the years, precisely by remaining a reigning dynasty.
And it is fortunate that the Bernadottes didn't go in the way of the Murats. In the case of the former, the issue obviously was not the sovereign status of the country itself (the Swedish monarchy is an old one, as I understand), as it was the fact that they were a parvenu house sitting on the throne. Interestingly enough, the 1823 marriage of the then-crown prince (future King Oscar I) was to a princess of Leuchtenberg who had more blue blood in her ancestry than her husband (whose parents, the king and queen, were both born commoners).
But that was because the Beauharnais family had already established itself on the European royal scene, through the approval by King Maximilian I of Bavaria of the marriage between his daughter Auguste (Joséphine's mother) and Eugène, the highly-regarded stepson of the king's ally Napoleon. Maximilian I even made his son-in-law into the Duke of Leuchtenberg and Prince of Eichstätt. In so doing, he effectively made the Beauharnais into royals (look whom the other children married).
So in a sense, the Beauharnais family was the opposite of the Bernadotte: they were able to acquire thrones through intermarriage because they were already regarded as quasi-royals, thanks to the Bavarian king's patronage. The Bernadottes, by contrast, had to first acquire a throne before gradually getting accepted as royals by other European houses (despite the fact that the family technically and legally became royal from the accession of King Carl XIV Johan). In the next generation, the heir to the throne couldn't marry anybody other than a quasi-royal like Joséphine Beauharnais. After that, however, the house had no trouble in intermarrying with other established dynasties.
Especially since they've managed to retain their reigning status.
The Murats were just upstarts only recognized by the Napoleonic Empire and its satelites, who never mingled with other royal families.
Even the Bernadottes, though adopted by the last swedish king, had a bit of trouble to be accepted at the royal "market".
Only at the 3rd generation did they join the royal merry-go-round.