In short, not that many. I don't think you'll find anyone who's willing to claim that Shrek's heart wasn't in the right place, but unfortunately he just wasn't equipped to effectively enact change in the political system of Far Far Away. Having lived the life of an Ogre in a swamp for most of his life left him with a thorough understanding of Ogre Issues, but unfortunately left him lacking in any formal political training. After the rigmarole that led to his ascension as king, Shrek was overall a beloved but ineffective king. Fiona, meanwhile, grew up locked in a tower all her life and thus couldn't provide him with much aid in matters of governance. Her experiences with Ogredom were limited as well - having only been turned into an Ogre a few years before. And, well, her experiences as an Ogre weren't exactly representative. Before the Shrekian dynasty, it was unheard of for an Ogre to reach the upper crusts of society, let alone for them to be king or queen. Thus her view on Ogre Issues was coloured by her own privileged past. Try as she might, she never really got the full picture.

In the end, Shrek never managed to gain the influence was unable to gather the political willpower to pass any Ogre discrimination laws. Shrek's blunt ways upset the political class of Far Far Away and notably him replacing all of his political aids and advisers with a donkey, a cat and a gingerbread man, well... it didn't really help. Shrek's predecessor had already struggled with republican agitation on the one hand and laissez-faire proponents on the other. While he was able to hold off these factions, they managed to capitalise on Shrek's inexperience and strenuous claim to the throne to push their agenda - an agenda which mainly focussed on turning the king into a figurehead.

Anything Shrek did achieve with regards to Ogre rights was indirect. The laissez-faire proponents' focus on promoting industry drew many citizens from the countryside to the new industrial cities, easing the pressure on the many Ogres living in various swamps somewhat. Raids on swamps also decreased in frequency, if only because it was hard to justify routine attacks on Ogres when the very coins the soldiers were paid with had an Ogre's face on them. But all in all, Shrek should've been able to do more. While there was obviously a great deal of pride in the Ogre community about one of their own reaching such a position in society, the consensus - as much as there's ever a consensus in the Ogre community - was that Shrek I's reign was overall disappointing.

Sources: ANDERSEN (H. C.), "Shrek is love", Far Far Away, Long Long Ago

GRIMM (W.) & GRIMM (J.), "Shrek is life", Far Far Away, Long Long Ago