I have XP Pro SP3 and Firefox 52.5.2 ESR, whilst I don't have the Home page open every time I start firefox, I use an App called OneTab in which I have a listing of commonly visited pages and that works for me reasonably well.
I have that set as my home page but don't have it set to open, I have Firefox start with tabs that were Show Windows and Tabs from last time. For me that is better than just having a single tab opening.
That said I'm currently not using the latest avast version I'm holding on to 17.8.2318.
EDIT: I have just tested having my Home Page display on startup and it works.
I also have 4 pinned tabs and even with a Home page set to display on restart, they were all present also. You could use this as a workaround have your Home page opened and pin it, if you don't find the cause.