Was there the idea of "peaceful Crusades"?

Was there the idea of "peaceful Crusades", which had symbolic meanings for pilgrims, or was it just the political invasion of Palestine territory, initiated by religious people (Pope Sylvester II and then Pope Urban II)?

No, no and no.

Peaceful crusades is a concept that is quite modern, kind of flower power 'let's all be friends' concept.

The Crusades were called for because of mistreatment and extortion of pilgrims to the holy lands (they had been conquered centuries before) and a real danger of muslim invasion of the Byzantine empire. What was left of it. That's the first no.

It was certainly not a political invasion (2nd no). The participating nobles gained territory, but that was a side effect. Not the main purpose. Even missionary efforts were limited or almost absent. The main purpose was to give pilgrims access to the holy lands. Everything else was extra.

The third no is for Palestine territory. It didn't exist at the time. Neither did political invasions in that time period. One conquered territory to gain something (im)material. For example land, peasants, cattle, prestige or wealth. Not to include it politically in one's fiefdom.

You're looking at history from a very modern viewpoint. That doesn't work.

Christendom had got too many bad news for centuries. Muslim conquest, dhimmitude, lost territories, persecuted churches. Arabia Petra, Levant, Jerusalem, Syria, North Africa, Sicily, Crete, Spain, all lost, eastern, western and heretics alike. Rampant piracy and slave taking raids. A Muslim base in south France for 80 years (Fraxinetum). Muslim raid of Rome itself. Too much. Plus, Vikings and Baltic Slavic Pagan raids, the Great Heathen Army, etc.

Then Manzikert happened, and the Eastern Empire was itself in danger, and had asked help from the Pope. Plus, some important symbolic churches in the holy land were destroyed by a zealous sultan. What could the Pope do?

Some good news were coming: Some french nobles (mostly non-primogenit sons that would not inherit any land, and so could only hope to be governors or advisors for their titled fathers and brothers) decided to go to Iberia with a bunch of knights and kick some Muslim ass. The Iberian kings consented and even granted titles to some successful helpers. The Pope sent his blessings.

The best example is Henry of Burgundy, who thought that being a Count under the king of Leon, ruling over lands captured from the Muslims, was better than being just the brother of the Duke of Burgundy. His grandson afterwards thought that declaring himself to be an independent king (Portugal) was even nicer, but this would be after the crusades.

The popes were too used to kings which would fight each other, drink, hunt and ignore the larger peril just because it did not threaten them immediately. Or, that would be afraid of leaving their lands to fight, lest their enemies attack them.

Suddenly, there were instances of successful cooperation, over large distances (France->Iberia). Finally some results!

So, Pope in 109X just went to france to give this example a very strong push to generalize it!! Make the nobles swear to help. Make them swear to keep peace while their neighbor is away crusading. Find someone to coordinate their efforts and financing. Make them understand that if they do not work together they may fall one by one.

So, to answer directly your question, no, the pope did not call for a peaceful pilgrimage. Moreover, the same zealous sultan who destroyed churches also made the former usual pilgrimages to the holy land more difficult. You can find some versions of the Pope original speech

https://en.wikipedia.org/wiki/Council_of_Clermont#Speech

You should read them with a grain of salt as there are only secondary sources left. but the general idea should be correct as there are various agreeing sources.

For your brethren who live in the east are in urgent need of your help, and you must hasten to give them the aid which has often been promised them. For, as the most of you have heard, the Turks and Arabs have attacked them and have conquered the territory of Romania [the Greek empire] as far west as the shore of the Mediterranean and the Hellespont, which is called the Arm of St. George. They have occupied more and more of the lands of those Christians, and have overcome them in seven battles. They have killed and captured many, and have destroyed the churches and devastated the empire. If you permit them to continue thus for awhile with impurity, the faithful of God will be much more widely attacked by them. On this account I, or rather the Lord, beseech you as Christ's heralds to publish this everywhere and to persuade all people of whatever rank, foot-soldiers and knights, poor and rich, to carry aid promptly to those Christians and to destroy that vile race from the lands of our friends.

And even the crazed children or peasant crusades did not hope to win without fighting. They just expected to win in some miraculous way.

The only instances of peaceful "crusade" I know come from the Franciscans:

St Francis, who went behind the crusader lines directly to the Sultan tent, trying to convert the Sultan himself (and the Sultan just expelled him back).

Ramon Lull, who considered the Muslims just a strong christian heresy, even if more distant than previous heresies (a position with many valid points) and wanted to convert them by preaching. He studied for many years, even convinced Universities to study Arabic to help the conversion of Muslims, and went himself to Tunis - from where he was banished after debating theology with Imams in Arabic He was beheaded on his third preaching trip, when he was 80+ y old.

The Franciscans also made other direct attempts to convert Muslims in North Africa. The five martyrs of Morocco are maybe the most known example, they are buried in Santa Cruz Church at Coimbra. They just went straight to Morocco to preach publicly. Portuguese merchants and mercenaries advised them to stop, before the inevitable execution happened. This was 1210, contemporary with the crusades.

But I do not think they would call these conversion efforts as "Crusades". Besides, Ramon Lull is at the end of c XIII, it may be considered after the crusades time.

BTW, these Franciscan efforts are directly related with them being granted custody of the christian holy places by future sultans

(and I am not giving direct references as you can easily google the names)