I have a sewer gas smell in the bathroom on the other side of the house when we use the washing machine. We replaced the wax ring on the toilet because we thought the smell was coming from there and the smell was gone for a few days and now it is back.

If the new seal solved the problem temporarily , then the problem is most likely the wax seal. Does the flange sit atop the finished floor ? Is the toilet sit rock solid or does it have a bit of wobble ? Did you use a standard wax seal - extra thick seal- seal with a plastic funnel ?

I would check for a dry floor drain somewhere in the vicinity. A dry trap can cause the same effect, especially if you generally have negative pressure in your drains. When the washer flows, it can push more air than the drain is usually sucking and the result is a puff of sewer gas during large water volume flows.

KCRoto makes a lot of sense. Also look for the possiblilty of a long tail piece from a sink. When they are too long the water falls with such speed and force that it can wash out the trap seal.