It's not at all necessary to have a virus-free citrus tree. What is important is to not have it infected by one of the viruses which damage the particular rootstock you are using. There are four "major" ones in the US, and a few minor ones.

Of all of them, Tristeza is the only one carried by insects (aphids), so your tree could "catch" it in your yard. And then, it would have to come from a neighbor's tree, since the aphids don't travel far. Tristeza will cause decline of trees on sour orange or C. macrophylla roots. Most other commonly used stocks are tolerant. Grapefruit and Key lime are also highly susceptible as rootstocks, but most people don't use them as stocks. On the other hand, if you're making a "fruit cocktail" tree, it's best not to use one of those two under another graft, for the reason of tristeza.

Psorosis is perhaps the "worst" of all the viruses, in that it causes decline regardless of stock or scion used. But it has been eliminated from nearly all commercial citrus, and is spread only by grafting of infected tissue. So the only way you're likely to acquire it is to graft from an old tree that has had it for many years, but has not yet declined to the point that you wouldn't take budwood from it. A rare situation these days. In Florida, that would mean budding from a tree of 'Thompson' pink grapefruit or 'Temple' orange (tangor) that is older than the mid-1980s. I'm not sure about remaining sources of infection in other states.

Exocortis is a viroid, and it affects Poncirus trifoliata (including Flying Dragon) and its hybrids (citranges). Some of the citrumelos (e.g., 'Swingle') are somewhat tolerant of most strains, but I'd still avoid it on those roots. Exocortis is acquired through infected budwood, AND can be spread on knives, pruners, or other cutting devices. So if you have one tree with the disease and you prune it, then another tree, there is the possibility of moving the disease from tree to tree, mechanically.

Xyloporosis is also a viroid and spreads like exocortis -- infected budwood or mechanically. However, it is not as easy to spread mechanically (lower percentage of infections per cut). It affects some mandarins and most mandarin hybrids, on any rootstock. It, too, has become rare in commercial citrus, so, like psorosis, the place you're likely to encounter it is to get wood from an old tree in someone's yard. HOWEVER -- other scions are tolerant, so it is possible that it's lurking in an orange, grapefruit, lemon, etc., and when you make that "fruit cocktail" tree, you move it into your tangelo accidentally.

Citrus ringspot affects any scion on any stock, but is quite rare. You're not likely to see it in the US. It does exist in a very small population of Texas and Florida grapefruit.

Milam decline is thought probably to be a virus, and affects any scion on 'Milam' lemon rootstock. All other combinations are tolerant. It seems to spread only in infected budding tissue.

So, in the long run, tristeza is the only virus to really worry about in the garden (realize that canker and greening are not viruses), and then, tristeza will only be spreading if it is already in the neighborhood. That's a major concern in Florida and some counties of California.

If your concern is canker and greening, rather than specifically viruses, then consider:

Canker is caused by a bacterium which comes to the surface of leaves and fruits and can be in water dripping or blowing through the tree. It can also be picked up on your hands or any other object that touches the infected tree, and transferred to another tree. It's not likely to be a problem on houseplants kept indoors, nor in dry climates, since it only spreads or activates in wet weather. But because of its easy mechanical spread, it is perhaps the most contagious of all the citrus diseases.

Greening is also caused by a bacterium, but is NOT spread mechanically. It spreads only in infected budwood during grafting, or by psyllid insects, which are not present in most States. We do have psyllids all over the citrus-growing region of Florida, so they can spread the disease if it is present in the area. The annoying thing about greening is that a tree can be infected and contagious for quite a long time before the first symptoms show up, so that allows it to move through an area undetected until it's way too late.