I cut a steak up into small strips with a pair of scissors.
Fried it in a pan with olive oil and onions.
Tasted great.
Until my wife told me I didn’t use the food scissors. I used the “house” scissors. We open packages, plastic, zip ties, etc all with the “house” scissors.
Should I be worried that I cut the steak with these? Will bacteria from the house scissors pass onto the steak? Or will the heat from frying kill it?
You will be fine.
The food was cooked...
Just clean the "house" scissors with soap and hot water and dry them so that there is no rust.
The concern for non-food scissors is generally not bacteria, particularly as you cooked it immediately after cooking, assuming you cooked it thoroughly.
The only real health concern would be what else you might have on the scissors. You might use non-food scissors to cut things that contain toxic chemicals, for example, or something else that could leech substances into your food that could be harmful. We can't advise you on that, given we don't know what you've done with your scissors. If you have any concerns, call your local Poison Control and they can give you advice for how to determine what the risk is.
The biggest definite problem is the scissors themselves - non-food scissors will be difficult to clean properly. Food scissors usually are able to be taken apart and put in the dishwasher, so the spot in between the blades can be fully cleaned (basically, two knives with a locking mechanism). Non-food scissors won't be able to be taken apart like that usually, and so will be very hard to fully clean. That may lead them to grow bacteria which could then cross-contaminate other things, going forward.
Bacterial (and other) infections are much more probabilistic than you appear to consider them. A few basic facts:
All pathogenic bacteria (and other pathogens) have a minimal infective dose, i.e., the minimal number of bacteria required to enter your body in order to start an infection. Fewer bacteria will not be able to cause an infection as your immune system reacts faster than the bacteria grow. The minimal infective dose varies strongly between different types of bacteria and depends on factors such as your immune system, but it rarely ever is 1, i.e., a single bacterium hardly ever suffices to infect you.
Bacteria are all over the place. They live on our skin, we carry around kilograms of them in our gut, they float around in the air, etc. I happen to know that there are roughly 10⁴ microbes (mostly bacteria) in each millilitre of my tap water (and I have no qualms drinking it as it is).
Most bacteria are not pathogenic, but are somewhere between not interacting with us at all and being symbiotic with us (the aforementioned kilograms of bacteria in our gut are an important part of our digestive system). In particular, to be pathogenic, a bacterium needs to be able to cope with a human as a host.
Cooking does not immediately kill all bacteria. Depending on the details of your process, a small fraction (something like 1 in 10⁶–10⁷) will survive the process (see this for some numbers). In particular, frying is not a very homogeneous process and thus there will likely be some bits that have non-vanishing probabilities of surviving bacteria.
The problem with your usual meat is that it is not sterile (free of microbes) and it is a perfect breeding ground for many bacteria, in particular those that like mammals (or at least vertebrates) as a host. Before your meat enters your pan, it will gather bacteria from the animal that provided the meat, the butchering process, etc. Those bacteria then have some time to multiply before you cook the meat, thus potentially reaching their minimal infective dose. By storing the meat in a fridge, you reduce this reproduction rate. By cooking the meat you ideally kill the vast majority, if not all of those bacteria, but even if a small amount survives or gets onto your food after cooking, it will probably not reach the minimal infective dose.
With all that being said, let’s finally turn to your scissors: Usually, they are far from a perfect breeding ground for bacteria, particularly those who like humans as a host, so any bacteria that got onto them due to whatever you did with them could not multiply. I presume you fried the meat immediately after cutting, so they had no time to multiply on the meat either. Finally, the frying process should kill of most, if not all of those bacteria. Thus, you will most likely be below the minimal infective dose. With respect to bacteria, the scissors are probably not much worse than any other of your kitchen utensils, let alone you. (As already noted, you should consider toxic substances on your scissors.)
Now, the above assumes that you had not done anything with your scissors that would expose them to a lot of pathogenic bacteria or make them a good breeding ground for them – such as cutting a steak with them: After your stunt, your scissors would be covered with liquids from the meat providing a perfect breeding ground for (pathogenic) bacteria. They are also likely to have acquired some pathogenic bacteria from the steak, you, or your household. Finally, you probably do not store your scissors in the freezer (not that this alone would help). Thus, you should really make sure to thoroughly clean your scissors afterwards, lest you contaminate other things or infect somebody with them later.
After your stunt, your scissors would be covered with blood[...] they really won't be; there should be no blood left in any meat you buy as that would be potentially highly toxic and cause the meat to spoil very quickly. The "blood" in raw (or rare) meat is a protein called myoglobin. Still clean your scissors (scissors? Really?) but don't lose any sleep over getting icky blood all over your kitchen when you cut meat.