Procedural democracy DOES NOT equal liberalism/Islamism but simply an upholding of the basic principle of peaceful transfer of power through free and fair elections for ALL citizens irrespective of their ideologies.
Many aspects of the JUI-F's ideology may be unsavoury and illiberal for you but Maulana's father - Mufti Mahmood - was one of the architects of the 1973 constitution. He was the first elected chief minister of former NWFP (now Khyber Pakhtunkhwa) in alliance with the secular-nationalist National Awami Party (NAP) and resigned on principle when Bhutto dismissed the NAP's government in Balochistan and sent in the Army. Today, the successors of the NAP (PKMAP and ANP) are also supporting the march. He was a member of the Anti-Bhutto PNA movement but also opposed Zia's Martial Law. Maulana Fazlur Rahman himself went to jail during the MRD movement and remained committed to the alliance despite being offered a leadership role in the establishment backed Islami Jamhouri Ittehad (IJI). The party's role in the country's electoral history is as illustrious as anyone else.
Moreover, If you cannot stop fawning over Imran Khan for giving those sections of society who were backers of military rule a stake in the democratic system (you know, OUR people), then the JUI-F has given many many more religiously minded voters a stake in the electoral process as well. They too are citizens of this country and have as much right to live here within the confines of the constitution as anyone else. Has Maulana made compromises in the past? Yes he has. Will he do so in the future? Most probably. But please get off your high horse and stop judging people in the thick of the action from afar.
If liberalism/leftism (whatever that means) is important for you and you don't want to support the march, then that's absolutely fine.
Of course, its quite clear that this liberal-leftism does not include the right to free speech and expression, given the mainstream media blackout of the Azadi March (or the muzzling of the media in general for the past two years), it probably also doesn't include the attack on all institutions of liberal democracy (from the election commission to the courts) by the 'hybrid regime'.
At the end of the day, it probably just means you don't want to be ruled by the proverbial 'maulvi', you know, it probably just means social liberalism. I totally get it, I mean Ayub Khan and Musharraf were loved by the elites for the same reason and I myself have a bit of a soft corner for the former, but that's a different topic.
But if your liberal-leftism does spill over in to democracy sometime, then keep this in mind: JUI-F's azadi march represents the clearest articulation and defense of 'procedural' democracy and the constitution in this country's recent history. Their main demands are all about the non-intervention of the establishment in the electoral process, about making this process as transparent as possible and for the country to be run by its constitution.
If you don't like their use of the religion card (though everyone else does it), their social views etc. then that's fine, but please don't say that they are not democrats. Like it or not, the right is the vanguard of the democratic movement at this conjuncture.
Finally, please stop recalling the specter of the 'Iranian revolution'. Yes liberals and progressives were slaughtered by the Mullahs but the latter by no means have a monopoly over such actions. A more appropriate example for our context is the liberal betrayal of democracy in Egypt when liberals cheered the removal and murder of a democratically elected President through military action, the slaughter of hundreds of Muslim Brotherhood activists, the incarceration of thousands more and the imposition of a military-police state many times worse than Hosni Mobarak.
Hopefully nothing of the sort will happen here but this is just to remind you 'Is hamam mein hum sab nange hain'.