However when the British conquered Jerusalem they played it as a secular conquest. Is this really true?

It's complicated. The Department of Information liked the crusading theme and the British press went for it, but some of the higher ups in the military and government hated it.

The commander of the British forces who conquered Jerusalem, General Allenby, wanted to avoid any religious connotations whatsoever. He went to great lengths to avoid acting in any way that could be construed as him being any form of crusader. When the victory was celebrated in an official ceremony, a bishop and a French diplomat were banned from attending because they had expressed the view that his campaign was akin to a modern crusade. As Allenby advanced toward the city, the British government sent out this statement to the British press:

15 November 1917. 1.45 pm NOTICE TO THE PRESS. PRIVATE AND CONFIDENTIAL. (NOT FOR PUBLICATION OR COMMUNICATION) The attention of the Press is again drawn to the undesirability of publishing any article, paragraph or picture suggesting that military operations against Turkey are in any sense a Holy War, a modern Crusade, or have anything whatever to do with religious questions. The British Empire is said to contain a hundred million Mohammedan subjects of the King and it is obviously mischievous to suggest that our quarrel with Turkey is one between Christianity and Islam.

So there were certainly those in government, particularly on the military side of things, that wanted to avoid any suggestion that Allenby's campaign was even slightly a crusade. Unfortunately for Allenby and the authors of that statement, there were those in the Department of Information who saw differently and wanted the British press to run with the theme of crusading for the sake of morale. Prime Minister David Lloyd-George didn't help matters when, after Jerusalem's capture, he made a reference to the Crusades in his speech on Allenby's victory. It began by commissioning newspaper columns pointing out that some of the high ranking officers in the campaign had crusaders as ancestors, while another ran a story about British Christian troops praying in the holy places as the crusaders did. Then they commissioned a 40 minute propaganda film called The New Crusaders: With the British Forces on the Palestine Front. Whenever the government got a message complaining about the portrayal of the campaign as a crusade, the censors would entirely agree - the British Empire had a very large number of Muslim subjects, Muslim soldiers fighting for it, and some Muslim allies in the war and it was important not to alienate them. Despite this, the government and military high command seem to have been unwilling or unable to reign in the Department of Information. They certainly complained though. We don't know who made this comment (though it was attributed to a friend of Lord Milner) but it was printed in the Evening Standard in early November 1917:

Could not Press Censor explain to the Editor that comments of this nature are ill advised, in view of the fact that our nearest ally to this front is the King of the Hejaz and other chiefs of Arabia, who are strict Muhammadans and greatly revere Jerusalem and all places connected with our Lord...

But at the same time, the Department of Information was sending out letters like this:

However, it is particularly on the sentimental, romantic and religious side of the Palestine campaign that the Prime Minister and Buchan wish emphasis to be laid, especially in the ecclesiastical press, and if you will keep the crusading idea in mind as you write the article, I feel certain that the results will be what they want.

The Department of Information seems to have been under the false impression that the government and military wanted the press to run with a crusading theme for Allenby's campaign. But they didn't - they frequently described the alienation of Muslim subjects as a nightmare for the British Empire.

So it's complicated. The government did not have a coherent policy. The Department of Information was keen on the crusading theme and many British papers ran with it in their coverage. Allenby himself was not keen, nor were the diplomatic and government staff of areas with large Muslim populations, who greatly feared that the portrayal of the campaign as a holy war would harm morale among Muslim subjects and alienate them from British interests.