I think it does damage the Tories reputationaly because of the DUP's ultra-conservatism on social issues. Even if they don't want to impose abortion control or gay marriage bans on the rest of the UK, there is still guilt by association which will alienate some liberal Tories.
The thing the DUP have out of the deal is money. One billion pounds increases Govt funding by 10% nationally to the province. Now apparently there is a 'magic money tree' for Northern Ireland, even if the rest of the union still has austerity. This is not fair and will cause deserved resentment.
On the Northern Ireland peace process, it puts the Govt on shaky ground. Even if Northern Ireland is benefiting financially, the Prime Minister has lost any claim to impartiality and with the Brexit changes this is a delicate time.