Should political tensions in Gaza and Ukraine influence U.S. stocks? I believe political tensions will always influence the financial markets, its the nature of the system. The question is in fact, to what degree? The best we can hope for is having a plan in place to deal with the outcome.
There's no real reason why the tensions in these countries, real though they are, should affect stock prices in the US. Consumer confidence isn't affected, and few companies have any real stake in the region. Things might change if the US decides to intervene militarily, but without this I'd expect our market to remain stable.
The armed conflict between a group of combatants should not have any effect on the values of US companies, unless the US company has a physical presence in the war zone of the combatants or the actions of the combatants disrupt the supply chain of the US company. In the case of Gaza or the Ukraine neither is the case.
I feel that the stock market should not be influenced by the Gaza and Ukraine, but I highly doubt that it won't be. I think a lot of times the stock market is affected by things it really shouldn't be and that it just creates more problems that it does.