List all SPNs but filter out certain types of Service Classes

By "Service Classes", do you mean the first part of the service principal name?

kadmin/changepw, ldap/SRV02, Microsoft Virtual Console Service/SRV02, etc.?

Is your question really "how do I get a list of all AD objects that have a service principal name in a list of SPNs that we've created (i.e., specific to our AD)?" Or maybe "How do I get a list of all SPN names specific to our AD?"

Here's a crude way of getting a list of unique SPN classes. Run it one with an empty list to get a list of all SPN classes found in the current domain. Select the ones you don't want to see and add them to the list. Then rerun it to verify that the list contains what you want.

# any name in this list won't be included in the output
$NotThese = "TERMSRV", "Hyper-V Replica Service", "Microsoft Virtual System Migration Service"

# get a list of ALL SPN names used
$x = Get-ADObject -Filter * -properties serviceprincipalname |
        Select-Object -Expand serviceprincipalname |
            ForEach-Object{$_} 

# eliminate unwanted SPNs and duplicates
$WantedSpnNames = @{}
foreach ($spn in $x){
    ($sn,$rest) = $spn -split('/',2)
        if ($sn -notin $NotThese){
            $WantedSpnNames[$sn] = $true
        }
}
$y = $WantedSpnNames.Keys | Sort-Object     # add any names you DON'T want in your report to the $NotThese array!


### use this to get the information for the service you DO want
# List populated from limited AD used only for testing
# Your list of unwanted names will vary
$NotThese = "WSMAN", "kadmin", "GC", "Microsoft Virtual Console Service","HOST", "RPC", "RestrictedKrbHost", "DNS", "ldap", "TERMSRV", "Hyper-V Replica Service", "Microsoft Virtual System Migration Service"
get-adobject -filter * -Properties serviceprincipalname, objectcategory |
    ForEach-Object{
        $servicenames = @()
        foreach ($s in $_.serviceprincipalname){
            ($sn,$rest) = $s -split("/",2)
            if ($sn -notin $NotThese){
                $servicenames += $s
            }
        }
        if ($servicenames.count -gt 0){
            $_ | Select-Object  @{n='Object Name';e={$_.name}}, 
                                @{n="DN";e={$_.distinguishedName}},
                                @{n="objectCategory";e={$_.objectCategory -replace '^CN=(.+?)(?<!\\),.*','$1'}},
                                @{n="servicePrincipalNames";e={$servicenames -join ";"}}
        }
    } | export-csv c:\junk\SPNs.csv -NoTypeInformation

Keep in mind that the serviceprincipalname property is a multi-valued object. Each element must be examined.