Aren't antibiotic resistant probiotics dangerous?
Usually, resistance genes are located on plasmids---additional DNA rings in the bacterium that are part of the genome. These plasmids cause their own exchange with other bacteria, even from other species.

B. clausii, the probiotics organism in question here, appears to be special, though, in that it has no plasmids. His resistance genes come with the primary ring-shaped genome and should not be transferred via plasmid exchange to other bacteria. This doesn't rule out other means of gene transfer like phages or conjugation, however. In one study, it was unsuccessfully tried to transfer a macrolide resistance gene to other bacteria. They conclude


  A potential hazard is transfer of resistance to microorganisms
  pathogenic for humans. The risk that this event will occur and the
  consequences in terms of morbidity and mortality have not been
  evaluated. Parameters required for risk assessment include studies on
  the nature and mobility of the resistance genes of probiotics.


The only other paper on a B.clausii resistance gene didn't look at its transferability. That clearly shows we don't know enough.  

B. Bozdogan, S. Galopin, R. Leclercq: Characterization of a new erm-related macrolide resistance gene present in probiotic strains of Bacillus clausii. In: Applied and environmental microbiology. Band 70, Nummer 1, Januar 2004, S.&nbsp;280–284, {{ISSN|0099-2240}}. PMID 14711653. PMC 321311.