I transfer prints directly from the second fixing bath to the toner. No problems and no staining except in one case where the fix inadvertently got overused.
My workflow is as follows:
Develop, stop (acetic acid stop) and fix in bath one, which is Ilford Rapid Fixer or Hypam 1+9. (I've used other fixers in the past, including TF-4 with fine results too).
I then, usually, wash and dry the prints and select the ones that merit keeping. After I've collected a number of these (usually a days worth of toning), I'll have a toning session.
The toning sessions consists of:
Water soak (five minutes), fixing bath two (also Ilford Rapid Fixer or Hypam 1+9), selenium toner, water rinse, wash-aid and then final wash.
Note that not only do I transfer prints directly from the second fix to the toner, but I also replenish and reuse my toner indefinitely. I filter it through coffee filters or filter paper before and after each use. The black sediment that is filtered out is likely selenium bound to silver compounds in the carried-over fixer. The prints tone just fine and, most importantly, pass the tests for residual silver (and hypo) with flying colors.
When I decide to print and tone in a single session, instead of dividing my workflow into printing and toning sessions, my regime is as follows:
Develop, stop, fix one, water rinse in running water tray, 2 minutes, fix two, toner, water rinse again (I use the same running water tray, which is simply a tray with some drain holes drilled at the bottom front corner and a water feed from the opposite end), and, finally, a 60-minute wash.
No staining ever from this workflow either. Note that I add a water rinse between the two fixing baths. I'm not really sure this is necessary, but I've got the running-water tray there all the time and I figure removing some of those soluble silver halides before fix two can't hurt.
It's important to know that with a a one-bath fixing regime, the capacity of the fixer is rather low and staining in the toner will occur once the fixer is exhausted enough to leave behind silver-thiosulfate compounds that attract the toner. This can happen fairly early, even after only 10-12 8x10s per liter of working strength fixer. Also keep in mind that using Ilford Rapid Fix or Hypam at the 1+3 dilution makes it more acidic, which can cause staining too.
The usual culprits for stains from transferring prints directly from the fix to selenium toner are 1) inadequate fixing, either from exhausted fixer or too-short fixing times and 2) the fix being too acidic, which reacts with the toner causing a general, overall yellowing.
Washing before toning is certainly not going to harm anything, it's just an added step. And, it won't make up for inadequate fixing either, so watch your fixer capacities.
If you get staining of prints partway or most of the way through a session, but not earlier, it is almost certain that you've overused your fixer. Two-bath fixing helps a lot in this regard.
Hope this helps,
Doremus