I started MTX when my little one was two. Never had more infections on it (or any other drugs, except steroids) than without.
My Rheumy’s advice is that it’s NOT that you stop it with any old cold or virus, (and whose not going to kiss their kids!), but there are certain bacterial infections, and serious viruses, like the flu, measles, chickenpox, that require you to get prompt treatment with antibiotics and / or stop the dose.
My Rheumy generally lets me plough through taking MTX, biologics, whatever, unless it is something serious. I have had Dengue (the second time, which has about 10% incidence of haemorrahic fever - thankfully I didn’t get that!), Salmonella, any number of non-descript third world tummy bugs, and bacterial bronchitis on MTX (plus or minus a biologic).
Given the life I was living, these were, ahem, environmental infections - not from any of the medications I was taking.
i will admit, I always carried antibiotics, and as soon I was sure it was a likely bacterial tummy bug I wasn’t shy with them.
None of those were fun, but with the exception of the flu and the bacterial bronchitis (which took us a while to figure out), I wasn’t any sicker or for any longer than anyone else.
From what I’ve read, a very small percentage of people can get unusual bacterial infections that can become very serious - but it is a small proportion (you’d need to read the stiudies, but my memory is less than 1%. I haven’t had this experience and don’t know personally anyone who has, so I’m not sure if it is a susceptiblilty issue or how quickly / insistently you seek treatment at the start.
You’ve already had some great suggestions (general hygiene etc - and don’t stop kissing your kids!), but also, fear the disease, not the meds. The serious side effects are very rare, and the quality of life you can regain can be truly magical