Is it possible that antibiotic-resistant bacteria become stronger, that is harder for the immune system to combat?
Short answer: It depends on the species of bacteria, immune status of an individual, etc.
The authors of this article: The Complex Relationship between Virulence and Antibiotic Resistance (PubMed, 2017) make a vague conclusion that:
Increased virulence [the potential of certain bacteria to cause
disease] may naturally evolve in response to or concurrently with
increased antibiotic resistance...
In one study in mice, antibiotic-resistant bacteria were less virulent than the antibiotic-sensitive ones. Comparison of the virulence of methicillin-resistant [MRSA] and methicillin-sensitive Staphylococcus aureus [MSSA] (PubMed, 1994)
These results indicate that MRSA is less virulent than MSSA in
normal hosts, but that they are equally virulent in immunocompromised
It's not possible to make a general conclusion from a single animal study, though.
Another aspect is that bacteria resistant to one antibiotic are prone to become resistant to other antibiotics. Staphylococcus aureus can become resistant to methicillin (methicillin-resistant S. aureus or MRSA), vancomycin (VRSA) and several other antibiotics (PubMed, 2009). Furthermore, plasmids (the DNA particles in the bacteria that induce antibiotic-resistance) can spread to other species of bacteria, for example, from staphylococci to enterococci.
If there is a genetic component to fighting off bacterial infections, do the generations since antibiotics have a higher percentage of members who are not going to be as good as people were on average 90 or so years ago at dealing with infections?
Antibiotics helped to survive many "bacteria-sensitive" people, and their offsprings may be more sensitive too, so it is possible that today there are more individuals sensitive to bacteria than 90 years ago. However, according to one 2015 study in twins, variation in the human immune system is largely driven by non-heritable influences (Cell.com).