Planning on re-insulating my rim joists tomorrow (well, later today, I'm up late.)

I've only removed one of the old pieces batt-type insulation. Home was built in 1958. No idea when these batt pieces were put in. No markings on the insulation.

Could these have asbestos in them? Do I need to have them tested before I remove them all, or am I definitely in the clear?

[Yes, I know the only way to know for sure is to have it tested. Just looking for opinions from people that take asbestos seriously but not beyond overboard to the point where they're spending lots of money testing stuff that shouldn't have it in it.]

(BTW I know the tile in the pic likely has asbestos.)

 

Because asbestos is cheap it was found in many things, domestic floor tiles but mainly in ships, large government buildings, hospitals.
There is asbestos in the air we breath and it is all over the world.
It does us no harm as long as it is not worked on with power tools that create a dust. The occasional exposure to asbestos is OK.
Only if you work with it on a day to day basis is it a problem.
Removal and disposal should not be a problem.