Martian life, if any, should simply be "trained" to pry on the particularities of its own environment, not ours. There's a extremely low chance that it could survive and thrive on our warm planet. Add to the fact that lots of precautions will be in place, Martian life exploration can be considered very safe for Earthlings.
However... since life evolves to be successful in (almost) any environment, Martian life could just as well be trained exactly for these rare moments: to be dormant then suddenly pry on unsuspecting alien visitors that come snooping around... But then that would be the argument of a successful Ridley Scott movie franchise.
But if life doesn't readily emerge, then we don't have any evidence one way or another. However, the likelihood of encountering extraterrestrial life is also diminished.
"But", someone replies, "I'm talking about life forced to evolve under extreme and alien circumstances." But Earth has plenty of extreme environments, both now and especially early on, and scientists optimistic about the likelihood of spontaneous life are constantly equivocating those environments to others in our Solar system and beyond. Plus, let's not forget that the modern, biologically created Earth atmosphere is something of an extreme environment of it own. So no matter how you spin it (I'm too lazy to put down several other scenarios I've had in mind), the more likely we are to encounter extraterrestrial life, the more robust Earth life likely is.
Expecting the opposite would be like betting on a random path in a graph with millions of edges to be faster than a path that was optimized by billions of computers for billions of years.
It's not that old life optimized for killing the new life (it probably didn't because it doesn't seem to be a common enough occurence). It's that the new life would be very likely very bad at everything.
> I think it's unlikely we'd find an bacteria or virus that could successfully infect Earth based organisms in a way that threatens us.
Between human species on Earth. Humans in the Americas were not genetically distinct from their European cousins, thus a European virus could readily infect an American human and vice versa (Europeans were not wiped out because the diseases they acquired were not as deadly, such as syphilis).
Our immune systems are adaptive, but a bacteria/virus will be limited in it's ability to adapt. As such, it's pretty unlikely to be able to infect a complex, multicellular organism that it's never encountered before. The most likely vector for an attack is an alien bacteria that is able to rapidly transpose genetic code with earth-evolved bacteria and create a novel hybrid. Then you are dealing with a COV-19 type scenario.
That's not to say we couldn't inadvertently pick up a bioengineered complex organism from an advanced alien species - that would be a completely different story.