There is no such thing, generally speaking and outside of particular medical conditions, as a "strong" or "weak" immune system.

There are two different factors being smooshed together.

One factor is general health and healthcare. A healthier individual -- no dietary deficiencies, well-rested, medical conditions treated, etc.. will generally just fare better when exposed to a disease. People in richer countries typically have better health.

Take cholera as a classic example. To a person in good health with access to water, cholera is a bad time, but unlikely to kill you or do permanent harm. To a person who already had nutrient deficiencies without access to abundant, clean water, it's a potential death sentence. This doesn't mean someone from a rich country had a "stronger" immune system. That person was just able to refill their personal health bucket faster than it drained thanks to those resources available to them.

In some cases, this is literally true. For example, being underweight is a worse comorbidity than being overweight by a similar amount, all else being equal.

The other factor is the immune response. Immune response is about exposure and recovery. You gain immunity to the pathogens you are exposed to as part of the recovery process. There's very little correlation between having an immune response to one disease and being better at fighting off another, different disease (though with quite similar things like strains of the flu, there is benefit). There's no such thing as "exercise" for your immune system. There is no evidence of overall strengthening caused by more exposure and recovery. Occasional studies come out that try to make this claim, but nothing very convincing has ever happened. That immunity response, in some cases, can diminish over time without re-exposure. There is precisely one medically sound and safe way to promote immunity: vaccination to relevant pathogens.

But if we're talking about "Don't drink tap water in Mexico" kinds of situations, it may APPEAR that way.

The reason locals don't get sick from the things that hurt tourists is because... they do. They did. It already happened, you just didn't see it. If you take someone from a very rich, healthy place and someone from a poor, unhealthy place and locate them both to a foreign environment with background pathogens to which they are not exposed, both are likely to get sick.