Were the Beirut bombings in April and October 1983 precursors to

subsequent anti-American actions in the Middle East?

Yes, they can be considered precursors to subsequent anti-American actions in the Middle East, because they were likely perpetrated by Hezbollah, a Shia Islamist organization that operates in Lebanon, supported by Iran, and that is anti-American and Anti-Israel.

Explanation:

The fact is that the United States has had a difficult relation with Iran ever since Ruhollah Khomeini came to power and founded the Iranian Islamic Republic. Hezbollah, as an ally of Iran, is also anti-American and as said before, was likely the perpetrator of the bombings.

Ever since, there have been many instances of Iran-led, or Hezbollah-led, attacks against Americans in the Middle-East, or against American insterests and allies. For this reason, the Beirub bombings can be considered a precursor of more recent confrontations.