Does the Fidelius charm actually factor in here much?
Remember the Exact Words of the secret:
The Headquarters of the Order of the Phoenix may be found at number
twelve, Grimmauld Place, London.
So it's not that the Death Eaters don't know the location of the house per se (in fact, they do have placed observers right outside!) - they are "just" prevented from knowing that the Order is in there and cannot intentionally search the house for them.
But what if Bellatrix tries to visit the house without second thoughts about finding the Order (especially now that she has a reason to)? That does not violate the secret in any way. She may have been able to do so all along as far as the Fidelius is concerned. But would have instead been prevented from finding the Order by the second line of defense in form of the other protective charms.
Before Sirius' death, the Order seemed to trust these charms. However, at least some of them are apparently less well-researched than the Fidelius charm (for which the consequences of the death of the secret-keeper are known). On the other hand, it's not too far-fetched that some are somehow tied to the ownership of the things they protect. We know that "ownership affecting the effectiveness of some magic" is a thing from the Elder Wand, for example. The Order members probably know more instances of this and this is why they are worried about their protection becoming ineffective against the new owner of the house, Fidelius or not (which they expect to hold, for the moment at least, - they fear Bellatrix on the doorstep, not any other random Death Eater).