The tweet contained an open call for others to also collaborate. Is there any problem with SpaceX doing it or doing it first?

I have to admit I get a bit of a knee-jerk reaction about even the appearance of conflict of interest, but if money isn't changing hands then I can't see a problem really. Regulators regularly collaborate with stakeholders, so why not experts in peripheral / somewhat related fields?

And really, conflict of interest seems to not matter in the slightest in American politics, what with senators and bureaucrats and their spouses etc getting enormous grants and setting up "non-profits", there must be an enormous list of concerning conflicts worse than this.

Absolutely: having a fat dynamic and rolling stock portfolio of the companies whose market you regulate as a member of congress is indeed problematic - but this not what this post is about, is it?