I think its very very unlikely that teams such as Mercedes, Red Bull and Ferrari feel threathened competitively by Andretti-Caddilac in the short/medium term. They could all spend half a billion a year if it would be allowed, GM has no advantage over them. Also money doesn't equal success just as Toyota found out. The current top teams are so optimized organizationally, so purposely setup and equipped, have the very best people regarding talent and Formula 1 experience, and are managed so well (M+RB) and have the absolute best drivers under contract. No new team is going to rival that within 5 years.
I think they will all come around and welcome Andretti-Caddilac. There is so much to gain internationally to allow them in. Also for Mercedes to beat Caddilac on a regular basis for the next 5 years with more and more Americans tuning in..that'll be worth a fortune marketing-wise.