Why is it ok to pronounce apricot using both a short and long "a"
sound and not ok to use both for the word apron?

That is just the way the English language is, probably because it is
spoken by so many people (native speakers) on two continents and has
been influenced by foreign pronunciation of many words.  In America,
older pronunciations (and some verb forms) are still used that are no
longer current in the UK.  Many people pronounce the same word
differently depending on sound of the word preceding it or the company
they are in.
You might enjoy the examples of different pronunciation of words on this site:
http://www.usd.edu/~bwjames/humor/language.shtml