Answer
Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother, thank you for raising such questions and for your interest to be more knowledgeable about Islam.
As for the issues you have mentioned such as wearing hats or short trousers, growing beards and many others that are related to the shape or appearance of a Muslim, they are known as what may be called the “appearance following” or (alhady al-zhahir) in Arabic.
Concerning these matters, a Muslim should follow the authentic sources he knows and the scholars he trusts. So, we should not argue a lot concerning such matters.
Responding to your question, Dr. Salah Al-Sawi, the President of the Shari`ah Academy and the Secretary General for the Assembly of Muslim Jurists in America, stated,
Wearing hats is not one of the peculiar features that distinguish non-Muslims and, therefore, there is no harm in wearing them whether made of plastic or any other material.
It is worth mentioning that it is more appropriated for a Muslim to wear familiar clothes that his people wear. As for covering the head with coffeie or cap, that is familiar to Muslims, this is preferable according to Muslim norms, but it is not an obligation.
As for the prohibition of wearing trousers below the ankles, scholars are unanimous to the effect that it is prohibited if they are worn in arrogance. If the intention is devoid of any arrogance, scholars differed. But if you are able to avoid wearing them, it is preferable so that you get rid of the scholars’ difference.
As for letting the beard grow, it is the practice of the best Prophet (peace and blessings and be upon him) regardless that non-Muslims grow it or not.