Andraste didn't found the Chantry. Her personal connection to it is literally zero. There were a number of Andraste-worshipping cults around in the years following her death, and they didn't all preach the exact same things.
The one we know now as the Chantry is just the one that survived and became powerful by allying itself with the Orlesian empire.
Actually, no the Chantry was founded in Tevinter about 200 years before Drakon basically coopted it in Orlais. Seriously, the Chantry today is based off the chant of light and the teachings of the cult of the Maker founded by Hessarian. The Imperial Chantry has since drifted from that original point to where Hessarian is now more important then Andraste and Magic is allowed, and men are priests instead of women, but originally Drakon basically copied the Tevinter Cult of the Maker into the Chantry.
Is the Chantry racists? No. They allow elves as clergy and templars both. They have large numbers of CEs who are devout chantry followers-this is why I don't think the CEs in Orlais actually want independence, they see themselves as orlesian and what the rest of Orlais to treat them as such. Heck the Chant of Light specifically requires that all races on Thedas adopt it for the Maker to return, you can't very well accomplish that if you aren't trying to spread it to other races.
Sexist-Not really. It is a tradition based off the original Prophet Andraste being female that the reverend mothers and clerics and such are female. They allow men to join the clergy, but in respect to Andraste they don't allow them in positions of leadership. It is also somewhat in relation to Maferath and his betrayal, but it is more out of tradition then sexism.
Again with the fall of the Dales, irregardless of who started it, the chantry position was in the beginning seeking to spread their faith to all races-one of the tenents of their faith, they didn't care that they were elves or humans and later to self defense when the dalish were marching on Val Royeaux. Shartan is a common theme in history. A cultural group or subset rises up against you, you remove their symbols from history. You can cry and moan about it if you wish, but it was done because the elves rebelled, not because they were elves and the Chantry is racist.