How long did you leave the door to dry before varnishing it...depending on what type of wood and the thickness of the door it can take 3 to 4 weeks for it to dry out fully.
Even if it seems dry to the touch the middle of the wood could still be soaking wet,which if you paint or varnish too soon could lead to the problem you have now.
I restore sash windows and remove paint by hand,with a combination of hot air gun, scrapers,nitromors and wirewool.
Seen some doors come out great when dipped and others come out like a nightmare(fluffy,warped,joints opened up etc.etc.
Hard to tell from a photo exactly whats gone wrong...If it was me I would wait and see if any more streaks appear or patches where whatever they were dipped in bleads through the varnish.
If it does ,then the only way to get a good finish will be to remove it all and start again(if it appears all over the door)If you can sand down the affected areas and make it good then thats a bonus.
as its a door and you can remove it away from the house to minimise the dust going into the house when you sand it down.I would sand then brush off the worst,or use the hoover with a brush attachment then use a tack cloth.£2 for 5 at dulux center,then use white spirit before applying varnish.
Had a look at the varnish you are using and it says 2 maybe 3 coats should be enough...rub down using 240 or better still 320 paper...all you need to do is give the next coat a key...not remove the coat you just applied.
