Crucifix pendants were very common. In fact here in Scandinavia one of the main signs of Christianity's arrival is when they start showing up in the archaeological record. Around the same time the iconic Thor's Hammer pendants start showing up as well, as a reaction to that. (whether the reaction was imitation or a counter-reaction is less certain) Anyway, the variation in crucifix pendants through the Middle Ages is as large as it could be;you have the whole material spectrum ranging from iron, tin, lead, white metal, copper, bronze, silver and gold (probably wood too even if fewer of those have survived). In terms of craftsmanship you likewise have the whole range from crudely snipped-out crosses to intricate and ornate objects of art. (and these properties were rather orthogonal; this guy is made of solid silver but hardly the work of a master silversmith)

So the wide range of object value bears witness to the variety of classes owning such objects. Although the upper classes are of course rather over-represented in the archaeological record, not least since they more often had items in less-perishable materials like noble metals, and their environs (e.g. castles) are more likely to have been excavated (or looted).

The relationship between the church, religion and such displays of wealth was complicated though. The 12th century Saint Francis was famously ascetic and opposed to wealth. His followers did not merely take a vow of poverty, they practically venerated poverty. He attracted many followers, but his was not the only narrative going on. The church was massively wealthy. For instance, besides the mitre hat and crozier, the ecclesiastical ring was one of the main attributes of a bishop. As always, people had bling to mark their status. Saint Francis and his followers never criticized the clergy for their wealth though. One can find those who did among the heretics; for instance in his response to Henry of Lausanne (or Le Mans), William the Monk quotes the former as having held that "bishops and priests ought not to have benefices or wealth", and makes it clear that this is seen as an attack on the clergy. (although to my knowledge no-one was deemed a heretic for this alone; Henry and others like Peter of Bruys had many other doctrinal criticisms as well) On the whole, wealth was regarded more as an impediment to virtue than a requisite for it, but to a certain extent there was also a counter-narrative that the clothing should reflect one's virtue and status. For instance the Sumptuary Laws which became popular in the 14th century often prohibited prostitutes from wearing clothes and accessories deemed too expensive. Fallen women ought to be visibly distinct from virtuous, married ones. Such laws frequently banned even noble women (more often on economic than moral grounds) from wearing too fancy things, but such restrictions seem to have been frequently flaunted and today we read those laws more as a description of the ruling classes idea of how people ought to dress, than how they actually did dress.

Another aspect worth noting here is that medieval jewelry was "not merely bling." (to quote the head antiquarian of the Swedish History Museum) It could have talismanic/amuletic powers. (the difference in an academic context is that an amulet has writing, and could be things as simple as a folded piece of paper iwth sacred and magic words on it. Here's one) So, magical rings are not just something out of Tolkien or Wagner, but something which actually existed. And for more objects than just rings. This spanned a whole range of things though, from the simple and widespread belief that wearing a crucifix would help protect you against evil, to more heterodox things like this ring from Denmark which has the magic words "arota/agla gala laga" scrawled in runes on the back. (heterodox because this kind of thing was not officially sanctioned, yet not explicitly heretical either and quite popular)

Nobody was under the impression you were supposed to flaunt your piety. But when it comes to pilgrimages, people did want to show where they'd been and, since they didn't have Instagram, perhaps bring home something to show off. Religious relics would be well beyond the means of the average commoner, but what was not were pilgrim badges. Objects from the destination, often a pin or brooch, which you could wear and show where you'd been. An iconic and early one was the scallop shell, worn by those who'd gone on pilgrimages to Santiago de Compostela to venerate Saint James. (indeed the Great Scallop is also the 'Saint James Scallop' or 'Pilgrim Scallop' in multiple languages) For instance here's one they found just last October in a dig in Enköping here in Sweden, and is almost certainly a pilgrim badge. (the alternative of some medieval gourmet eating shellfish imported from afar seems much less likely) More often though, the badges were metal objects (like this) manufactured and sold at the pilgrimage site. Very much like many of today's souvenirs, these were cheap, mass-produced objects, cast out of lead or tin. Typically they depict the saint venerated at the pilgrimage destination and proved you'd been there. (until a certain trade in forged pilgrim badges developed, which the church naturally did its best to stop) This is not to say that the thing sold to pilgrims were limited to the badges, though.

Now when it comes to the relics; those were more often a way to attract pilgrims than the result of them. (although of course many visits to the holy land resulted in the bringing home a splinter of the True Cross and so on) Acquiring a significant relic for one's cathedral could lead to a great increase in pilgrims and hence tourism money. As a result there was quite a thriving trade in the medieval relics business. A lot could be written about that and has been written (e.g. Elizabeth Anne Wiedenheft's thesis Circulating saints: a study of the movement of corporeal relics in three regions of Western Europe, c. 800-1200, 2018) but that'd be going off on a tangent here.

So, in short, yes it was quite common to wear crucifixes and tokens of religious pilgrimages.

Source for the quote of William the Monk is Edward Peters, Heresy and Authority in Medieval Europe, 1980