During the 19th century when Italy was being unified into an independent state, the vast majority of Italians of the time would have been Catholic. I can't imagine that it would have sat well with many of them having to attack and conquer the leader of the Catholic Church.

That pope Pio IX wasn't exactly loved by the time of the breccia di porta pia and in general all the Italian risorgement was made against curch's wishes.

Let's go back of a few decades at the beginning Pio IX seemed the man that everything one hoped for introduced a constitution banish torture then in 1948 in the climate of revolution that was flaying over italy Carlo Alberto king of Sardinia-Piedmont attack the austrians the Pope send a contingent of troops that quickly retract this was seen as a treason and pushed the people of Rome to revolt and the Pope was forced to run. The repubblica romana was born that was able to resist for months against the troops of Napoleon III that were called by the Pope to regain the city. After the fall of the roman republic the Pope eliminated all the progressive reform and introduced the concept of Papal infallibility in a (doomed to fail) attempt to contrast the independence ideal. He quickly ended up to really despised.

Was it hard to inspire people to want to fight against the Papal forces?

No.There were many attempts to get the city between 1948 and the breccia di porta pia (rome annexation) all stopped by either french or piedmontese troops.

Did many Italians take up arms for the Papacy?

No not many. Actually the city was taken pretty easily thanks in part to the fact that Pio IX realised that holding the city. But is significative that the Pope tried to block the invasion menacing excommunication to whatever general will ever ordered tho fire on rome the problem was averted thanks to the fact that a Jewish general gave the order.

Did Papal resistance to Italian unification cause popular unrest in unified Italy during the early years of the new nation?

Unrest maybe is too strong word but the roman question definitely caused problems I'll copy paste here a comment that I wrote of the topic in the past :

when italy invaded and conquered the Vatican state the Pope declared himself a political prisoner inside the Vatican and declared that all good catholics should stay out the politics and priests discoraged people to vote (except in the areas where pro curch parties where prevalent obviously). Is easy to imagine the problems that this created in a mostly catholic country. The strategy that our first governaments followed basically this : let's ignore them the will calm down some day. After 70 years we admitted that this strategy wasn't working and so we passed from confrontation to appeasament. And during Mussolini era we signed the treaty called Patti lateranensi they got Vatican City , monetary refund for nationalised properties ,an "apology" for the invasion and to teach religious education in schools. Then after the war this treaty was inserted in the constitution since not even the communist party was eager to reopen that querrel. Then after some decades in the 70s the church started losing is grip traditional values become contested a more modern idea of society was born and contraceptives, abortions, divorces become allowed.

During the 80 the treaty of Patti lateranensi was rewritten: the refunding become volontary as religious education in schools. This negotiations appened during the Craxi era who was the first socialist italian pm.

And that's all I hope to having been useful op and sorry for eventual error in the writing.