What are things that liberals and conservatives have in common?

They are both human... well, so I'm told :P

breathing air................that may be it

In Australia, they're the same thing. The ultimate irony - the conservative party is called the Liberal Party. They're in power at the moment, led by a weak conservative moderate who has allowed the hard right of his party to emasculate him. He used to have principles, but has compromised all of them in order to hang on to the top job.
That's the core difference between American and British/Australian political systems (ours is based on the Brits - it's called the Westminster System). The Prime Minister (chief executive of government, the boss in most matters) is elected by the Party that holds a majority in the lower House, either in its own right, in coalition with one or more minor parties or by agreement with the crossbench that they will not obstruct legislation - that kind of minority, known as a "hung parliament", is always shaky, the crossbench then can hold the government to ransom. The PM can be thus dumped by his own caucus, which has happened three times in the last ten years - Kevin Rudd was replaced by Julia Gillard after losing the confidence of the Labor Party caucus (a stupid move, Rudd was popular with the electorate), then was reinstated when Julia was copping a hiding in the opinion polls. Tony Abbott was shafted by the Liberals when it became apparent that an electorate which only voted for him in the interest of stability (sick of Labor's "musical chairs" leadership) now universally hated him and the Party would have been routed in the upcoming election had he remained at the helm. Malcolm Turnbull held on by the skin of his teeth, the Liberal/National coalition has a majority in the House of ONE vote. The upper House is purely a house of review, it cannot create new legislation but can block bills.

There re both carbon products. 

 I'm proud to be an American,
where at least I know I'm free.
And I won't forget the men who died,
who gave that right to me.
~Lee Greenwood