Because religion is also a theory about how society should live, what is sacred/holy/profane/immoral/etc, not just what someone believes for themselves.
Plus, in a sense, he doesn't force his religious views on other people. He asks other people not to step on his religious concept (the marriage as a specific sacred mystery / holy union with specific rules, etc).
Now his objection might be outdated, but it's not some outlandish idea the "beyond the pale" kind, like being in the KKK. Just a few decades ago (not in some ancient ages) most of the US (not to mention the global population) would have agreed with this, including many progressives otherwise. Heck, it wasn't even one of the major demands of gay activists themselves back in the day.
In other words, can you please explain why priests should not be forced to marry gay couples? "Force" is a loaded word, of course - I'm not necessarily talking about armed agents going into a church and demanding that a priest perform a marriage ceremony, but rather referring to the full range of coercive actions available to the federal government. For example, if a church refuses to perform same-sex marriages, why should they get tax-exempt status?
Maybe churches shouldn't have tax exempt status at all. Taxing some religious organizations and not others sounds unconstitutional though.
Because part of the whole point of a religion / creed is that you do some things and not others.
"Forcing priests" means no freedom of religion expression, one of the older democratic rights.