My first pilgrimage was to Lourdes in the South of France - as a member of the German army. During an introduction course in the first weeks after joining the army we were told we were entitled to certain programs, and getting time off from the army. After basic training and entering regular service I went to the base's priest, told I'm I'm an atheist and that I'm interested in going to Lourdes. No problem. Best party of my life I must say, in a landscape straight from a movie (but I think I was the only one of ~35,000 soldier pilgrims to walk into the hills, even if they started right at the edge of town).
Second pilgrimage was with a Catholic girlfriend, walking from dawn to dusk to a Catholic pilgrimage destination for several days. Very strenuous. I even "spread god's word" in a sense, when towards the end somebody thought I still looked fresh and strong so I got to carry one of the loudspeaker backpacks used to spread the prayers spoken by a priest at the end of the procession along the long line of pilgrims :)
Nobody cares what you are. Just go if you want. There even are priests that are atheists: https://www.irishtimes.com/news/lutherans-in-a-quandary-over...
> Alarm bells started ringing in earnest last June, when the priest in question, Thorkild Grosboel, pastor of Taarbaek, a town near Copenhagen, went on to elaborate his views in an interview. "There is no heavenly God, there is no eternal life, there is no resurrection," he said, with typical Scandinavian matter of factness.
> Grosboel has since refused to step aside and insists that his lack of belief in some of the theological foundations on which the Christian church is built, does not stop him fulfilling the duties for which he is paid.