Should I be concerned about drinking tap water?

It really depends on the location. Sciencemag.org has an article on this, which is backed up by this paper. To quote a relevant part from sciencemag:

Allaire and her colleagues downloaded EPA’s data and looked at the number of health-related water quality violations for 17,900 community water systems in the continental United States over a 34-year period. Some were for elevated lead levels, the problem in Flint, but the data set also included violations for coliform bacteria—a group of microbes that is easy to detect and serves as an indicator of bacterial contamination in general—nitrates, arsenic, and other contaminants. The researchers combined those data with information from the U.S. census such as housing density and average household income, to figure out which communities were most vulnerable.

The following sentence from the significance page from the scientific article's website leads me to the conclusion that you shouldn't be worried per se, but that it is certainly worth looking into the situation in your area:

Here, we show that health-based drinking water quality violations are widespread, with 9–45 million people possibly affected during each of the past 34 years. While relatively few community water systems (3–10%) incur health-based violations in a given year, improved compliance is needed to ensure safe drinking water nationwide.

If there is something wrong with the water (as you might find after your research) then see what the specific advice is. Some things may go away after boiling, others may not.

Use this website by the EPA to search for the 'Consumer Confidence Report' on drinking water quality by the EPA.

I would ask your friends what evidence they have to support their opinions. They will be unlikely to produce anything besides conspiracy theory level information. It’s similar to the vaccine debate. Who do you believe? The large, established scientific community, or your friend’s hunch?

Tap water is regulated by state and federal governments for safety. Virtually all tap water in the US is absolutely safe to drink. Filters can improve taste, which is impacted by many factors, but neither home filters nor boiling would remedy a Flint, MI type contamination.

Mistrusting tap water would mean mistrusting our regulatory bodies (tempting right now, understandably) - but to do so would impact so much more than your tap water. It would be like rearranging deck chairs on the titanic to filter your tap water if you believe the the functionality of our government has so degraded. Meat, milk, household cleaners, detergents, eggs, bottled water, packaged and caned foods — all and more would also be compromised by regulatory corruption.

Also, the poor, hospitals, etc. depend on tap water — if it’a not safe, shouldn’t your friends and fellow citizens be more outraged? Even if they filter or boil it, they still pay for the water, shouldn’t they protest or complain to their provider?

US tap water is safe, drink away.

Have you considered simply taking a sample of your tap water to your local water company and requesting that it be tested? If you don't trust them to test it and give you the actual results, there are literally thousands of companies in America that will do this for you for a very small fee.