The judge didn't order him to testify she told him he'd had to show up if he wanted to proclaim executive privilege. The reason they will appeal is there is a two fold catch here. If he goes in and claims executive privilege there is a chance the committee will request a closed door hearing to determine that the testimony he'd give would fall under executive privilege. Meaning he'd had to testify to what he's holding as being privilege, which we all know how well that would work with all the leaking going on. That's why they will appeal this.

The attorney client privilege is also a two fold situation as again the attorney's could be pulled into a closed door hearing to determine if the information held applies to that privilege and/or if appealed the court could possibly determine a limitation prior to testifying a limitation on the information they could ask questions on. In Giuliani's case I would assume all the information he holds qualifies under attorney client privilege as what he gathered was a potential defense against anything that might have came in the way of the Mueller investigation if any criminal/wrong doing charges had came out of that. He had a right to investigate any other defense including that the Russian collusion narrative was a hoax and the only way to do that was to investigate and at least prove enough to produce a reasonable doubt in the mind of a jury. The big question that could lead to closed door testimony would be would the Biden aspect of Giuliani be part of the over all work product involved in building his defense against the Mueller investigation. I myself can see that as a possibility to some extent as if there was corruption on the part of the Bidens it was being hidden by and under the protection of then president Porshenko, as was the Soros involvement in all this...so there could be a compelling narrative to fix the 2016 election against Trump came as a matrix of interlinking reasons why they want Hillary to win over Trump. In a case such as that it would all fall under work product protected by attorney client privilege.

I would assume McGahn falls within the same boundaries but once again they could try and demand closed door hearing(s) to determine that. Regardless that's a slippery slope to go down as the 2016 election is under a criminal probe...and how that would all work into this....and just how much of that information needs to be protected to keep the dems from building yet another scenario to try and defend themselves against.

I don't think the fifth amendment plays much into this as the impeachment as it stands now has proven nothing in the way of high crimes and misdemeanors. Everything Ukraine related can be proven to have started before Biden announced his bid to run, which came four days after the Ukrainian president lost his re-election bid. If one wants to look for obstruction of justice it would seem that would be a good starting point as Biden had good reason to all of a sudden make that his chosen announcement date. He jumped into the race to obstruct the investigation being done by his opponent Trump and his attorney(s) who was facing potential charges stemming from the Mueller investigation. The fact that April was also the date the democrats changed the whistle blower law all reeks of yet another democratic operation to set up an alternate mechanism (scheme) to implement in case the Ukrainian president lost his re-election bid.