The DUP hold extremely socially conservative views that are not shared by the majority of the British electorate
They are extremely socially conservative
They are against LGBT rights
The former leader of the Party Ian Paisley launched a political campaign in 1977 called "Save Ulster from Sodomy", to prevent the decriminalization of homosexuality in Northern Ireland. As this article goes on to state:
Arlene Foster’s ultra-conservative Northern Irish party has previously
supported the introduction of a ‘conscience clause’ to protect
religious people who want to discriminate against anyone who is LGBT.
This means LGBT people could be refused service or turned down for
jobs simply because of their sexuality or gender.
The DUP has stalled all progress on equal marriage in Northern
Ireland, attempted to retain a lifetime ban on gay men giving blood,
and opposed same-sex couples adopting children.
This is problematic since the vast majority (over 90% given data was sampled in 2007 and since then trends show liberalisation of attitude), support LGBT rights in UK. If the conservative party did not criticize these views of the DUP they could risk massively damaging their credibility with their own voters in mainland UK.
Mainland UK has one of the most liberal abortion laws in Europe, and the vast majority of voters support abortion in Britain. Again not openly opposing the DUP's stances would risk conservative votes in the UK, and they could be punished for such stances next time they go to the polls.
The DUP also has a reputation for climate denial, in 2008 the DUP's environment minister said
I still think man-made climate change is a con
As the governments own public attitudes survey by the Department of Energy and Climate Change says (emphasis mine)
The level of concern over climate change has risen slightly at wave
17, increasing from 66% at wave 13 to 70% at the latest wave. Levels
of concern over climate change were highest amongst 55 -64 year olds
(80%), those earning over £35,000 per year (77%), and social grades AB
(76%) and C1 (76%). Concern was lowest amongst social renters (57%)
and those in social grades DE (57%). Respondents were more likely to
see climate change as a result of human activity compared with natural
processes. Four in ten (43%) believe it is caused mainly by human
activity,compared to only one in ten (10%) that believe it is mainly
down to natural processes. Four in ten think it is caused by a mixture
of human activity and natural causes (41%).
As you can see not only are the majority of British voters believers of climate change but concern is highest amongst 55-64 year olds. Older voters especially tend to vote for the conservatives, so they aren't going to sacrifice their own votes to support climate denial for this Irish party.
Finally the DUP has links to paramilitary groups and endorsements from such terrorist organisations, as this article states
The UDA is less known in England than the IRA, largely because they killed Northern Irish Catholics during the Troubles, which didn’t make the news as often as the killing of English people or security personnel. The UDA is a violent loyalist paramilitary group, which is still active today. Just weeks ago, it murdered a man in broad daylight in Northern Ireland. The man was shot dead in a Sainsbury’s car park in front of horrified shoppers and his three-year-old son.
The UDA backed the DUP in this election by issuing a statement in support of the party’s South Belfast candidate Emma Little Pengelly, “strongly urging” people to back her.
One of the frequent things that conservative supporting news outlets and one of the bastions of conservative attack was the Labour leader Jeremy Corbyns supposed support of the IRA (an Irish paramilitary organisation), if the Conservatives sign a deal with the DUP. He can just as easily turn around and say look your "friends and allies" support paramilitary organisations in Ireland.
TLDR: The DUP are considered radically to the right of British politics, and refusing to condemn them would cost the conservatives a huge number of votes in mainland UK, ergo they will oppose them.