After searching various different resources, I am still confused as to why Hermione thought that bringing Yaxley inside the Fidelius charm cast on Grimmauld Place would comprimise the safety of the place.
As mentioned earlier in The Deathly Hallows, Hermione voices concern over how safe a refuge it is given that Snape is able to enter, but is reassured that he would be driven off by the defensive spells in the hall. However, surely it must of occurred to at least one of them that he could bring other Death Eaters into the house if it were possible. The apparition would not stop Voldemort for long, even though according to Dumbledore he
"secretly fears [the dead]".
At this point they believe him to be a loyal servant of the Dark Lord. As a master of non-verbal spells, Snape wouldn't even need to speak in order to bring other Death Eaters in/bring Harry out of safety to Voldemort. If bringing people inside by apparition was possible, why would Snape not just appear elsewhere in the house with Voldemort, or, if this was not possible and the doorstep was the only possible place to apparate to, to there, then proceed to have one of the most powerful Dark wizards of the age dismantle the spells on the door/blow said door of its hinges?
Given this, why are they so utterly certain that Yaxley would be bringing in Death Eaters via side-along apparition after their botched escape from the Ministry of Magic? The spells Moody put in the hall to guard against Snape acted against anyone who entered, including them. If the trio considered them enough to keep Snape out, why not Yaxely? Did they believe that the sight of Dumbledore would unsettle Snape enough to force him out, but no one else?
Additionally, surely the case of Snape and Yaxley is different? Snape was a "second generation" Secret Keeper - that is, he was informed of the location by Dumbledore (he must have been to be able to enter prior to Dumbledore's death), the original Secret Keeper. This is the same as Ron, Hermione and Harry. But Yaxley must be a "third generation" Secret Keeper having been shown the place by Hermione. No "second generation" Secret Keeper could divulge the secret of No. 12 Grimmauld Place while the Dumbledore was alive, so why could Yaxley have passed on the location given that more "senior" Secret Keepers were still alive? This could be a result of the "dilution" of the protection described by Lupin(?) when explaining why it had been abandoned as headquarters, but is there any evidence to support this?
Sorry that is so long. I have looked on the wiki and searched in Google but there don't seem to be any conclusive answers.