The key to suppressing them is obviously to find out where they comes from. I know that Mudcat uses Google Adsense (GA) to insert adverts, and I checked that, on Android, Firefox Tracking Protection (TP) suppresses the adverts I see - but they are not pulldowns. (That's with AdBlock Plus turned off; probably ABP will block them on it's own but I didn't check.)

So are these pull-downs generated by GA as implemented on Mudcat or are they inserted by something else? I don't know how you'd find out on an iPad (examine the page source?) but if they don't occur on other sites I'd guess they are generated by GA.

TP uses a blocklist, and has various setting - or it does on desktops:
A closer look at Firefox's Tracking Protection

So I'd guess that by changing the settings you changed the blocklist. Or maybe the blocklist got updated: if these adverts are intermittent it could be that some ad servers are on the list and some not.

Whether an 'external' ad blocker app will stop them on Safari will depend on how it works. Some have whitelists of 'allowed' adverts - but you can usually turn that off and block everything. That's the case with AdBlock Plus which I use. ABP also has an 'acceptable ads' policy - and from your description these would not be acceptable. But I know nothing about ad blockers on iOS.