Centrism is arguable two things; one an electoral strategy and one a very broad ideology. The former would refer essentially to not being a purity candidate and adjusting to the views/whims/superstitions of the electorate; so I’d imagine Blair for example was less socially conservative than he presented himself to the electorate and likewise Brown was less fiscally conservative than he would have portrayed himself in the late-90’s. Centrism as an ideology on the other hand acknowledges that both markets and governments have their strengths and their failures and as such rejects socialism and libertarianism, instead opting for a mixed economy the balance of which ranges from anywhere between Thatcherism or Cameronism to the “Nordic model”.
This, inadvertently exposes the core problem of centrism.
Thatcherism, aka Reganism, aka market economics, aka neo liberalism, advocates (amongst other things) the complete handover of virtually all state functions and assets to the market, the destruction of organised labour and the reduction of the role of the individual to consumer and provider of services and labour to private interests. This is an extreme, radical position.
The opposite position to this is the abolition of private property, the seizure of the means of production and management of the state and its assets by the proletariat, or, as it is commonly known, communism.
The centrepoint of these positions is some variety of socialism, or if you shift somewhat to the right - the nordic model - state managed capitalism.
Yet the centrist automatically selects radical neo liberalism as one pole and state managed capitalism as the other. This is why they so readily accommodate fascism, because their reflexive inability to consider left economic solutions mirrors fascism's hatred of same. For the centrist, capitalism, no matter how extreme, is the only game in town and they will pick jackboots over communes every time.