Yes, candidates for President should be allowed to receive foreign funding, because ultimately, it doesn't change the vote of the people. Trump won the Presidency. He spent one of the least amounts of any candidate for president in recent times. Ultimately money spent doesn't change the will of the people, so foreign donations don't make a significant difference.
Candidates for President of the U.S. should receive funding from any legal source, even it the source is foreign. If we try to control where funding comes from it opens an entirely unworkable can of worms. There is no chance on earth that regulating such funding can ever be tracked and effective.
2016 shows how foreigners may take over American society, Funneled through nondescript entities, Or stated ones. Russia, Or Saudi Arabia, Does it matter? Both are foreigners and have no business using their dollars to influence, Or take over American elections. For which party is irrelevant. American electorate under control of foreigners, Or other nonvoters is philosophical coup, Equivalent to warfare; financial warfare for control of American government. Goodbye freedom!
U.S. political candidates may legally take donations from American citizens or from permanent residents of the United States wherever they happen to live, even if the money is raised overseas. Many people also will recall the "Chinese money" scandal that erupted during Bill Clinton’s 1996 reelection campaign. The Democratic National Committee returned $3 million in illegal or otherwise questionable contributions after much of it was discovered to be from foreign nationals.
I believe that for several reasons it would be unwise to allow any Presidential candidates to receive funding from foreign countries. There is no way that accusations of impropriety could be avoided, the candidate would then feel beholden to these outside interests in lieu of the favours that they had received.