The summer is a very good time to get some basic maintenance and repair work done on your furnace. This is for several reasons. First off, your furnace needs regular maintenance to continue working the way you would like. Even if you do some of the basic maintenance yourself — some of which is very easy for you to do, and worth learning how — there's more extensive maintenance that it will need. Furnaces need to be cleaned regularly, for example. Basic maintenance also serves another purpose. It helps get someone else's eyes on the inside of the system, and they'll be able to spot some issues before they morph into problems.
This can save you a lot of future stress. Sometimes issues compound each other, so catching an issue early on can save you from having more widespread repairs — so this may even safe you money. Because it's the off season, you won't have to handle the issue quite so urgently, and even if it's not going to be cheap, you can still take some time and put some money back so that the repair doesn't hit your finances quite so hard. Also, you won't have to deal with being cold while you're waiting for costly furnace repairs. That will reduce stress in the whole household.
But setting all of that aside, poorly maintained furnaces can be dangerous. This is true any time you're dealing with something that uses an open flame or a lot of heat. A dirty or poorly maintained furnace can cause a house fire, for example. Gas furnaces can leak, you can get carbon monoxide in your home. Carbon monoxide is a very dangerous gas; you can't smell it or see it, and it can cause you a lot of harm.
If you're not staying on top changing your filter frequently, you're going to get a lot of particulates in the air, which isn't good for anybody. It is particularly not going to be good for anybody with a sensitive lung situation, like asthma, damage from COVID-19, allergies, respiratory disease, and so on.
The intent is not to scare you. While these can happen, the most likely situation is that your furnace will just break. There can be serious results from not staying on top of your maintenance, and that's important information to know so you can make the best decision for you and your household. Contact an HVAC contractor to learn more about furnace maintenance.