As a retired career Federal Employee I will say that our union had warned us years ago to be very careful what we tweeted/FB'd/put 'out there'. But this was more about IF a client or someone we were investigating 'found us' there should be nothing there that disparaged the Agency or was vulgar/obscene by 'community standards'. Expressing a political opinion in one's private life is a protected activity under the Hatch Act. Doing it on official time or presenting it as approved by the Agency one works for is not.
So IMO Strzok and Page were engaging in protected activity as long as the tweets weren't done on official time or posted via Govt computers or phones. BUT, we all know that what we post online can come back to bite us in the ass, so in that context they probably should have mentioned them before accepting posts in Mueller's Investigation. In such a sensitive position I'm sure they were asked "Is there anything we should know before you accept this job?".
But what really gets me is the inference that ANY Federal employee, let alone an FBI agent, is incapable of doing their job impartially, regardless of their political beliefs. God knows I worked through Administrations and policies that I absolutely abhorred, but by God I did my job impartially and to the best of my ability and prayed for better times.