You may want to look through this page and some of the sources there: https://en.prolewiki.org/wiki/Anti-base_movement (and of course, anyone is welcome to add missing examples to this page)
I'm quickly writing much of this from memory so please double-check any claims I make here. The articles linked are not necessarily Marxist sources but just general sources touching on the issues mentioned. Here are some concerns in no specific order:
Sovereignty, local law, and Status of Forces Agreements. Look into SOFAs and the legal impunity and privileges that they often confer on US personnel abroad. This results in a variety of issues such as US soldiers committing violent crimes against citizens without being held accountable, to things like contractors being able to enter the country with no inspections or visas, to certain facilities such as local airports becoming lily pad bases for US forces. Read: Why does the US have a military base in Ghana? for some examples. Read about extraterritoriality as the more general term for this kind of legal exemption and about "lily pad bases" for examples of de facto US bases which are not necessarily officially designated as such.
War provocations. Countries become bases from which to launch attacks at US enemies, as well as becoming potential targets. People generally do not want their homes to become a launchpad nor target for wars between other countries. Read: Living at the tip of the spear: Guam and restraint.
Health and environmental harm. Military bases are a risk to the environment, especially in colonized places where the occupying power has no real care to take any precautions to protect human health nor the natural environment. Read up on this case where jet fuel from a US military base in Hawaii leaked into the water supply and caused violent illness for thousands of people, and threatens to pollute the main aquifer of Oʻahu: How Hawaii Activists Helped Force The Military’s Hand On Red Hill. In fact, US military activity in the Pacific has regularly threatened aquifers, such as the US bombing range on Kahoʻolawe cracking the island's sole source aquifer, making the island unable to hold fresh water anymore. Pollution from the RIMPAC exercises also litters the ocean with toxic substances, with the exercises including the practice of hauling old boats out to sea and torpedoing them until they sink and will leech various substances into the water. Also it should be noted that some of the supposed "environmental protection" laws that the US will put in place surrounding its bases are actually meant to disrupt local peoples' access to subsistence fishing, traditional ecological practices, or other such activities, for example in the case of Diego Garcia the prevention of subsistence fishing would make it hard for the forcibly expelled population to return and sustain themselves.
Destruction of cultural, historical, archeological, ancestral, and spiritual sites. Many US bases have been placed or are planned to be built on important sites which carry cultural or other significance to the local population. Even bases which are now closed have left behind unexploded ordinance and/or pollution which makes the areas unusable, inaccessible, or renders important sites desecrated or destroyed. Some examples I can think of at the moment are Makua Valley in Hawaii and Ritidian in Guam.
Displacement from homes. People have frequently been displaced from their homes in order to construct bases, often by forcible expulsion and occasionally with the untrue promise that they would be allowed to return to the land eventually. There are many examples of this but forced expulsion in Vieques in Puerto Rico is one example, so is the case of the people from the Chagos Islands who were forcibly expelled and then dumped in another country to make way for the US-UK base at Diego Garcia. Read: Stealing a Nation and The Toxic Legacy of U.S. Foreign Policy in Vieques, Puerto Rico.
Safety hazards. There are various cases of people being killed or wounded by errant bombs from US bombing ranges, such as in Korea and Puerto Rico. Read up on the Maehyang-ri Kooni Firing Range: Bombing ends, but village still not free from past. Residents of Maehyang-ri suffered deaths and lifelong injuries from errant bombs, extreme noise exposure, psychological damage, a heightened suicide rate, and pollution of the land and sea which harmed health and made their village's fishing products undesirable. Unexploded ordinance also leaves behind a major hazard, making areas of an occupied country unsafe to enter for locals for many decades, such as with various sites in Hawaii mentioned before, but many other sites in many countries have faced this issue.
Violent crimes. As mentioned before, SOFA agreements create impunity or near-impunity for US personnel. There are numerous cases of murders as well as killings by negligence, and sex crimes committed by US personnel. Read about the killing of Jennifer Laude in the Philippines (this is a Wikipedia link, I don't have an article on hand), US military sex crimes in Okinawa, the two middle school girls run over by the US military vehicle in Korea. There is also this article, Welcome to the Monkey House, detailing the state-sanctioned brothels set up in south Korea for the benefit of the US military, with impoverished women and orphan girls coerced and trapped into living in zones surrounding US military bases as "sex workers" who would even be medicated, inspected, and tagged by the government to do this.
I have certainly overlooked something here but I hope this gives you some jumping off points.
Still slowly going through the books I mentioned in a previous thread (The Kaiser’s Holocaust: Germany’s Forgotten Genocide and the Colonial Roots of Nazism, and Civilian-Driven Violence and the Genocide of Indigenous Peoples in Settler Societies). Set them aside for a little bit because I started reading The Devil's Milk: A Social History of Rubber as I was looking for some historical information on rubber production. I think today I'll pick one of these three and make some more progress in it.